Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C53×#2115 ⋊ C2 |
| Sylow | C53 ⋊ #33532 |
1090 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1090 conjugacy classes of subgroups — too many to draw. Only its 183 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)(57,71)(62,86)(67,97)(72,76)(73,102)(83,113)(87,91)(88,106)(94,96)(98,100)(99,107)(103,108)(104,110)(105,112)(114,116)(115,117);(54,57)(55,62)(56,67)(58,76)(59,73)(60,71)(61,83)(63,91)(64,88)(65,86)(66,94)(68,100)(69,97)(70,99)(72,79)(74,108)(75,110)(77,102)(78,112)(80,106)(81,107)(82,98)(84,113)(85,114)(87,92)(89,105)(90,117)(93,116)(95,96)(101,115)(103,109)(104,111);(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)(55,61)(57,67)(58,75)(59,81)(60,69)(62,83)(63,90)(64,93)(65,84)(66,74)(68,78)(70,77)(71,97)(72,104)(73,107)(76,110)(79,111)(80,85)(82,89)(86,113)(87,115)(88,116)(91,117)(92,101)(94,108)(95,109)(96,103)(98,105)(99,102)(100,112)(106,114);(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)(54,55,60,65)(56,66,69,95)(57,62,71,86)(58,74,79,109)(59,80,77,64)(61,82,84,68)(63,89,92,78)(67,96,97,94)(70,101,81,90)(72,103,76,108)(73,106,102,88)(75,93,111,85)(83,100,113,98)(87,112,91,105)(99,117,107,115)(104,116,110,114)Polycyclic presentation:
2^8,53|a^2=h,e^2=gh,g^2=h,b^a=be,c^a=cf,e^a=eg,g^a=gh,i^a=i^52,e^b=eg,f^b=fh,g^b=gh,i^b=i^52,d^c=dh,e^c=eh1184 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 323479);