Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
| direct product | #41×Dic137 |
| Sylow | C137 ⋊ C4×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D137 |
| commutator | C2×C137 | C23×C4 |
| Frattini | C22 | C23×D137 |
| Fitting | C2×#41×C137 | C2 |
| socle | C22×C137 | C24 |
| hypercenter | C2×#41 | D137 |
| hypocenter | C137 | C4×#41 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
310 conjugacy classes of subgroups.
1400 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #104×Dic137, #31780601, #31780807, … |
| maximal normal subgroup of | #104×Dic137, #31780601, #31780807, … |
| maximal quotient of | #117×Dic137, C4×D4×Dic137, C4×Q8×Dic137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1020);