Finite Group DatabasebetaFinite Group Databasebeta| order | 7856 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C8×C491 ⋊ C2 |
| Sylow | C491 ⋊ M16 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C2×D491 |
| commutator, socle | C2×C491 | C2×C4 |
| Fitting | C8×C491 | C2 |
| hypercenter | C8 | D491 |
| hypocenter | C491 | M16 |
| LCS | G ▷ C2×C491 ▷ C491 | |
| UCS | C1 ◁ C4 ◁ C8 | |
20 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,491|a^2=c,c^2=d,b^a=bd,e^b=e^4901970 conjugacy classes. The character table is too large to display.
| maximal subgroup of | M16×D491, C2×#21463311, #30628343, … |
| maximal normal subgroup of | M16×D491, C2×#21463311, #30628343, … |
| maximal quotient of | #30628247, (C2×D491)⋊C8, Dic491⋊C8, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7856, 23);