Finite Group DatabasebetaFinite Group Databasebeta| order | 7856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| direct product | C8×D491 |
| Fitting | C8×C491 ⋊ C2 |
| derived, Sylow | C491 ⋊ C2×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C8 | D491 |
| commutator, hypocenter | C491 | C2×C8 |
| Frattini | C4 | C2×D491 |
| Fitting | C8×C491 | C2 |
| socle | C2×C491 | C2×C4 |
| LCS | G ▷ C491 | |
| UCS | C1 ◁ C8 | |
22 conjugacy classes of subgroups.
1976 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C16×D491, #30628276, C2×C8×D491, … |
| maximal normal subgroup of | C16×D491, #30628276, C2×C8×D491, … |
| maximal quotient of | C8×Dic491, (C2×D491)⋊C8, Dic491⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7856, 21);