Finite Group DatabasebetaFinite Group Databasebeta| order | 7856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | D4×D491 |
| Fitting | D4×C491 ⋊ C2 |
| Sylow | C491 ⋊ C2×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D491 |
| commutator, socle | C2×C491 | C23 |
| Fitting | D4×C491 | C2 |
| hypercenter | D4 | D491 |
| hypocenter | C491 | C2×D4 |
| LCS | G ▷ C2×C491 ▷ C491 | |
| UCS | C1 ◁ C2 ◁ D4 | |
54 conjugacy classes of subgroups.
1235 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8×D491, SD16×D491, #30628361, … |
| maximal normal subgroup of | D8×D491, SD16×D491, #30628361, … |
| maximal quotient of | C22⋊C4×D491, C4⋊C4×D491, (C22⋊D491)⋊C4, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7856, 34);