Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C53×#2170 ⋊ C2 |
| Sylow | C53 ⋊ #33860 |
636 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 636 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 — 4 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)(54,58)(55,64)(56,71)(57,68)(59,85)(60,75)(61,90)(62,82)(63,93)(65,98)(66,79)(67,78)(69,103)(70,97)(72,110)(73,108)(74,109)(76,111)(77,99)(80,84)(81,87)(83,96)(86,107)(88,117)(89,102)(91,112)(92,116)(94,105)(95,114)(100,115)(101,113)(104,106);(54,57,62,64)(55,58,68,82)(56,70,74,76)(59,77,88,96)(60,79,61,78)(63,92,95,80)(65,81,100,107)(66,90,67,75)(69,102,104,108)(71,97,109,111)(72,105,91,113)(73,103,89,106)(83,85,99,117)(84,93,116,114)(86,98,87,115)(94,112,101,110);(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)(54,56,62,74)(55,63,68,95)(57,76,64,70)(58,80,82,92)(59,84,88,116)(60,73,61,89)(65,97,100,111)(66,94,67,101)(69,99,104,83)(71,107,109,81)(72,86,91,87)(75,112,90,110)(77,114,96,93)(78,103,79,106)(85,108,117,102)(98,105,115,113);(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)(54,55,62,68)(56,69,74,104)(57,75,64,90)(58,79,82,78)(59,83,88,99)(60,67,61,66)(63,91,95,72)(65,86,100,87)(70,71,76,109)(73,111,89,97)(77,107,96,81)(80,114,92,93)(84,101,116,94)(85,98,117,115)(102,103,108,106)(105,110,113,112)Polycyclic presentation:
2^8,53|a^2=h,b^2=h,c^2=h,e^2=gh,f^2=h,g^2=h,b^a=be,c^a=cf,d^a=dg,e^a=eg,f^a=fh,g^a=gh,i^a=i^52,c^b=ch,d^b=de,e^b=eg,g^b=gh,i^b=i^52,f^c=fh,e^d=eg,g^d=gh,i^d=i^521499 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 326383);