Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C53 ⋊ #11650 |
304 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 304 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) = 101 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 3 generators on 101 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)(56,62)(59,65)(63,68)(66,69)(70,73,76,75)(71,78,80,91)(72,82,85,84)(74,86,90,89)(77,92,93,94)(79,87,96,97)(81,95,98,101)(83,99,100,88);(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)(55,59)(57,63)(58,62)(60,66)(61,65)(64,68)(67,69)(70,72,76,85)(71,77,80,93)(73,84,75,82)(74,88,90,99)(78,94,91,92)(79,95,96,101)(81,97,98,87)(83,86,100,89);(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)(54,55,57,60,58,61,64,67)(56,59,63,66,62,65,68,69)(70,71)(72,81)(73,78)(74,87)(75,91)(76,80)(77,83)(79,89)(82,95)(84,101)(85,98)(86,96)(88,94)(90,97)(92,99)(93,100)Polycyclic presentation:
2^8,53|a^2=e,b^2=h,c^2=h,d^2=fh,e^2=g,f^2=h,b^a=bd,d^a=df,f^a=fh,i^a=i^52,c^b=cgh,d^b=df,f^b=fh,i^b=i^522138 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 79566);