Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C4×C8×C137 ⋊ C2 |
| Sylow | C137 ⋊ #436 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C22×D137 |
| commutator, socle | C22×C137 | C22×C4 |
| Fitting | C4×C8×C137 | C2 |
| hypercenter | C4×C8 | D137 |
| hypocenter | C137 | #436 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C4 ◁ C4×C8 | |
122 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=e,c^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^136,c^b=cf,g^b=g^1362204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778746, #31778748, #31779618, … |
| maximal normal subgroup of | #31778746, #31778748, #31779618, … |
| maximal quotient of | #31779675, #31779681, #31779687, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 628);