Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C53 ⋊ #12617 |
382 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 151 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 — 3 generators on 117 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)(54,57,59,75,60,77,81,107,61,76,82,106,58,74,79,104)(55,63,65,89,66,91,95,116,67,90,96,115,64,88,93,113)(56,69,71,98,70,73,100,102,72,99,80,109,78,103,83,105)(62,84,85,110,68,87,97,111,86,101,94,117,92,112,108,114);(54,56)(55,62)(57,73,76,103)(58,78)(59,80)(60,70)(61,72)(63,87,90,112)(64,92)(65,94)(66,68)(67,86)(69,77,99,74)(71,82)(75,105,106,102)(79,100)(81,83)(84,91,101,88)(85,96)(89,114,115,111)(93,97)(95,108)(98,104,109,107)(110,113,117,116);(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)(54,55,59,65,60,66,81,95,61,67,82,96,58,64,79,93)(56,68,71,97,70,86,100,94,72,92,80,108,78,62,83,85)(57,63,75,89,77,91,107,116,76,90,106,115,74,88,104,113)(69,87,98,111,73,101,102,117,99,112,109,114,103,84,105,110)Polycyclic presentation:
2^8,53|a^2=e,b^2=f,c^2=e,d^2=h,e^2=g,g^2=h,b^a=bd,i^a=i^52,c^b=cg,d^b=dh,e^b=eh,f^c=fh,i^c=i^521208 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 84690);