Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C53×#504 ⋊ C2 |
| Sylow | C53 ⋊ #33385 |
1114 conjugacy classes of subgroups; only the 351 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 351 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 117 |
| transitive degree | μt(G) = 3392 |
A minimal faithful permutation representation — 4 generators on 117 points:
(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)(57,72)(63,87)(68,95)(73,99)(74,75)(83,108)(88,111)(89,104)(92,113)(96,115)(97,105)(100,116)(101,117)(102,103)(109,110)(112,114);(54,57)(55,63)(56,68)(58,73)(59,74)(60,75)(61,72)(62,83)(64,88)(65,89)(66,87)(67,92)(69,96)(70,97)(71,95)(76,100)(77,101)(78,102)(79,103)(80,99)(81,104)(82,105)(84,109)(85,110)(86,108)(90,112)(91,111)(93,114)(94,113)(98,115)(106,116)(107,117);(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)(54,56)(55,62)(57,68)(58,77)(59,70)(60,82)(61,71)(63,83)(64,90)(65,84)(66,86)(67,76)(69,79)(72,95)(73,101)(74,97)(75,105)(78,98)(80,107)(81,85)(87,108)(88,112)(89,109)(91,93)(92,100)(94,106)(96,103)(99,117)(102,115)(104,110)(111,114)(113,116);(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)(54,55,59,65,61,66,60,81)(56,67,70,93,71,94,82,90)(57,63,74,89,72,87,75,104)(58,76,78,91,80,106,79,64)(62,77,84,98,86,107,85,69)(68,92,97,114,95,113,105,112)(73,100,102,111,99,116,103,88)(83,101,109,115,108,117,110,96)Polycyclic presentation:
2^8,53|a^2=f,e^2=gh,f^2=h,g^2=h,b^a=be,e^a=eg,g^a=gh,i^a=i^52,e^b=eg,g^b=gh,i^b=i^52,d^c=dh2144 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 322502);