Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C53 ⋊ #7387 |
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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 — 2 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)(54,56)(55,62)(57,75)(58,70)(59,83)(60,71)(61,73)(63,89)(64,85)(65,87)(66,95)(67,88)(68,74)(69,77)(72,84)(76,99)(78,108)(79,110)(80,102)(81,103)(82,86)(90,96)(91,117)(92,116)(93,114)(94,115)(97,105)(98,107)(100,112)(101,111)(104,106)(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)(54,55,58,64,60,65,80,93,61,67,81,94,84,66,59,82)(56,68,70,96,71,97,102,116,73,98,103,117,72,104,83,89)(57,74,76,90,78,105,111,92,79,107,112,91,113,106,77,63)(62,75,85,99,87,108,114,101,88,110,115,100,95,109,86,69)Polycyclic presentation:
2^8,53|a^2=d,c^2=eg,d^2=f,e^2=gh,f^2=h,g^2=h,b^a=bc,c^a=ce,e^a=eg,g^a=gh,i^a=i^52,c^b=ce,e^b=eg,g^b=gh1220 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 57030);