Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| isoclinism | isoclinic class of D53 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C32 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C32×Dic53 |
| derived, Sylow | C53 ⋊ C2×C4×C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C32 | D53 |
| commutator, hypocenter | C53 | C2×C4×C32 |
| Frattini | C2×C16 | C22×D53 |
| Fitting | C22×C32×C53 | C2 |
| socle, prime radical | C23×C53 | C2×C16 |
| cosocle | C2×C16×C53 | C23 |
| LCS | G ▷ C53 | |
| UCS | C1 ◁ C22×C32 | |
270 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 195 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 91 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 91 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)(56,57,58,59);(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)(60,61,62,66,63,67,70,76,64,68,71,77,73,79,82,86,65,69,72,78,74,80,83,87,75,81,84,88,85,89,90,91);(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, 89737);