Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C53×#1381 ⋊ C2 |
| Sylow | C53 ⋊ #12829 |
378 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 103 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)(55,62)(56,67)(58,77)(59,82)(60,72)(61,83)(63,87)(64,90)(65,91)(66,92)(68,100)(69,95)(70,103)(71,75)(73,79)(74,78)(76,110)(80,112)(81,86)(84,115)(85,116)(88,107)(89,117)(93,114)(94,98)(96,102)(97,101)(99,105)(104,108)(106,111)(109,113);(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)(54,56,59,70,60,69,78,101)(55,61,81,93,63,66,65,85)(57,67,82,103,72,95,74,97)(58,76,79,111,80,68,99,102)(62,83,86,114,87,92,91,116)(64,89,108,109,88,84,75,98)(71,94,90,117,104,113,107,115)(73,106,112,100,105,96,77,110);(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)(54,55)(56,66,69,61)(57,71)(58,75)(59,81)(60,63)(62,73)(64,79)(65,78)(67,94,95,113)(68,98,76,109)(70,85,101,93)(72,104)(74,107)(77,91)(80,108)(82,90)(83,96,92,106)(84,102,89,111)(86,112)(87,105)(88,99)(97,115,103,117)(100,114,110,116)Polycyclic presentation:
2^8,53|a^2=f,b^2=dg,e^2=gh,g^2=h,b^a=bd,c^a=ce,d^a=dh,e^a=eg,g^a=gh,i^a=i^52,e^b=eh,f^b=fh,i^b=i^52,d^c=dh,e^c=eg,g^c=gh,i^c=i^521190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 85708);