Finite Group DatabasebetaFinite Group Databasebeta| order | 8656 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C22×Dic541 |
| derived, Sylow | C541 ⋊ C22×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C23 | D541 |
| commutator, hypocenter | C541 | C22×C4 |
| Frattini | C2 | C22×D541 |
| Fitting, socle | C23×C541 | C2 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C23 | |
54 conjugacy classes of subgroups.
2176 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31772535, C2×C4×Dic541, C2×#22575813, … |
| maximal normal subgroup of | #31772535, C2×C4×Dic541, C2×#22575813, … |
| maximal quotient of | C2×C4×Dic541, C2×C22⋊Dic541, C2×C4⋊Dic541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8656, 33);