Finite Group DatabasebetaFinite Group Databasebeta| order | 8768 |
| isoclinism | isoclinic class of D137 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C8 · Schur multiplier (H2) = C26 |
| direct product | C22×C8×D137 |
| Fitting | C22×C8×C137 ⋊ C2 |
| derived, Sylow | C137 ⋊ C23×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C8 | D137 |
| commutator, hypocenter | C137 | C23×C8 |
| Frattini | C4 | C23×D137 |
| Fitting | C22×C8×C137 | C2 |
| socle | C23×C137 | C2×C4 |
| LCS | G ▷ C137 | |
| UCS | C1 ◁ C22×C8 | |
338 conjugacy classes of subgroups.
2240 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #336×D137, #31780484, #340×D137, … |
| maximal normal subgroup of | #336×D137, #31780484, #340×D137, … |
| maximal quotient of | C2×C4×C8×D137, C22×C8×Dic137, C2×C22⋊C8×D137, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8768, 1305);