Finite Group DatabasebetaFinite Group Databasebeta| order | 8416 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×C8×D263 |
| Fitting | C2×C8×C263 ⋊ C2 |
| derived, Sylow | C263 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | D263 |
| commutator, hypocenter | C263 | C22×C8 |
| Frattini | C4 | C22×D263 |
| Fitting | C2×C8×C263 | C2 |
| socle | C22×C263 | C2×C4 |
| LCS | G ▷ C263 | |
| UCS | C1 ◁ C2×C8 | |
76 conjugacy classes of subgroups.
2128 conjugacy classes. The character table is too large to display.
| maximal subgroup of | (C2×D263)⋊C16, C4×C8×D263, #97×D263, … |
| maximal normal subgroup of | (C2×D263)⋊C16, C4×C8×D263, #97×D263, … |
| maximal quotient of | C4×C8×D263, C2×C8×Dic263, C22⋊C8×D263, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8416, 147);