Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C42 · Schur multiplier (H2) = C214×C4 |
| direct product | C23×C42×D53 |
| Fitting | C23×C42×C53 ⋊ C2 |
| derived, Sylow | C53 ⋊ C24×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23×C42 | D53 |
| commutator, hypocenter | C53 | C24×C42 |
| Frattini | C22 | C25×D53 |
| Fitting | C23×C42×C53 | C2 |
| socle | C25×C53 | C23 |
| prime radical | C25×D53 | C22 |
| cosocle | C22×C53 | C26 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C23×C42 | |
24030 conjugacy classes of subgroups; only the 13515 normal subgroups are shown.
This group has 24030 conjugacy classes of subgroups — too many to draw. Only its 13515 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 67 |
| transitive degree | μt(G) = 6784 |
A minimal faithful permutation representation — 6 generators on 67 points:
(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);(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)(64,65,66,67);(60,61,62,63);(58,59);(56,57);(54,55)3584 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1076116);