Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#20272900 |
| Fitting | C22×C32×C53 ⋊ C2 |
| Sylow | C53 ⋊ C2×#1417 |
294 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 119 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 119 points:
(1,2)(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)(56,58)(57,63)(59,76)(60,71)(61,83)(62,74)(64,90)(65,86)(66,95)(67,97)(68,88)(69,75)(70,79)(72,77)(73,81)(78,109)(80,111)(82,87)(84,102)(85,89)(91,103)(92,118)(93,117)(94,115)(96,119)(98,106)(99,108)(100,116)(101,114)(104,112)(105,107)(110,113);(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)(56,57,60,65,62,68,81,67)(58,69,71,98,74,99,73,105)(59,75,78,106,80,108,113,107)(61,82,77,66,84,94,112,96)(63,85,86,101,88,100,97,70)(64,89,91,114,93,116,92,79)(72,103,102,117,104,118,83,90)(76,95,109,115,111,119,110,87);(54,55)3404 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 90020);