Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Sylow | C137 ⋊ #379 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D137 |
| commutator | C22×C137 | C22×C4 |
| Fitting | C25×C137 | C2 |
| socle | C23×C137 | C23 |
| hypercenter | C25 | D137 |
| hypocenter | C137 | #379 |
| LCS | G ▷ C22×C137 ▷ C137 | |
| UCS | C1 ◁ C23 ◁ C25 | |
506 conjugacy classes of subgroups.
Polycyclic presentation:
2^6,137|a^2=f,b^a=bd,c^a=ce,g^a=g^1362204 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31778693, #31780703, #31780704, … |
| maximal normal subgroup of | #31778693, #31780703, #31780704, … |
| maximal quotient of | #31779012, #31779030, #31779060, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 405);