Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C53×SD128 ⋊ C2 |
| Sylow | C53 ⋊ #13743 |
126 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 39 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 181 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 181 points:
(2,3)(4,5)(6,7)(8,9)(10,11)(12,13)(14,15)(16,17)(18,19)(20,21)(22,23)(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)(42,43)(44,45)(46,47)(48,49)(50,51)(52,53)(55,63)(62,92)(64,96)(65,97)(66,98)(67,90)(68,107)(74,106)(81,140)(86,148)(93,152)(94,153)(95,105)(99,155)(100,156)(101,150)(102,157)(103,141)(104,158)(108,170)(109,121)(114,176)(118,178)(122,168)(123,169)(124,138)(134,171)(142,146)(154,164)(159,163)(161,177)(165,167);(1,2,4,6,8,10,12,14,16,18,20,22,24,26,28,30,32,34,36,38,40,42,44,46,48,50,52,53,51,49,47,45,43,41,39,37,35,33,31,29,27,25,23,21,19,17,15,13,11,9,7,5,3)(54,56,61,73)(55,62,63,92)(57,75,80,128)(58,82,85,145)(59,87,89,149)(60,91,88,72)(64,99,96,155)(65,102,97,157)(66,104,98,158)(67,105,90,95)(68,106,107,74)(69,110,113,77)(70,115,117,76)(71,119,120,83)(78,135,137,181)(79,139,136,127)(81,93,140,152)(84,147,130,144)(86,94,148,153)(100,161,156,177)(101,163,150,159)(103,167,141,165)(108,171,170,134)(109,124,121,138)(111,174,175,160)(112,133,151,162)(114,168,176,122)(116,131,143,166)(118,169,178,123)(125,173,179,129)(126,172,180,132)(142,164,146,154);(54,55)(56,68)(57,74)(58,81)(59,86)(60,90)(61,63)(62,69)(64,77)(65,76)(66,83)(67,88)(70,114)(71,118)(72,121)(73,107)(75,102)(78,134)(79,138)(80,106)(82,99)(84,146)(85,140)(87,108)(89,148)(91,109)(92,113)(93,126)(94,125)(95,151)(96,110)(97,115)(98,119)(100,160)(101,162)(103,166)(104,111)(105,112)(116,177)(117,176)(120,178)(122,129)(123,132)(124,136)(127,167)(128,157)(130,142)(131,141)(133,150)(135,164)(137,171)(139,165)(143,161)(144,163)(145,155)(147,159)(149,170)(152,180)(153,179)(154,181)(156,174)(158,175)(168,173)(169,172)Polycyclic presentation:
2^8,53|b^2=h,d^2=ef,e^2=fg,f^2=gh,g^2=h,b^a=bd,c^a=ch,d^a=de,e^a=ef,f^a=fg,g^a=gh,d^b=de,e^b=ef,f^b=fg,g^b=gh,i^c=i^52956 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90629);