Finite Group DatabasebetaFinite Group Databasebeta| order | 7856 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | C2×C4×C491 ⋊ C2 |
| Sylow | C491 ⋊ #41 |
| subgroup | G/H | |
|---|---|---|
| center | C4 | C2×D491 |
| commutator, socle | C2×C491 | C23 |
| Frattini | C2 | C22×D491 |
| Fitting | C2×C4×C491 | C2 |
| hypercenter | C2×C4 | D491 |
| hypocenter | C491 | #41 |
| LCS | G ▷ C2×C491 ▷ C491 | |
| UCS | C1 ◁ C4 ◁ C2×C4 | |
40 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,491|c^2=d,b^a=bd,e^b=e^4901970 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30628263, #30628265, #30628343, … |
| maximal normal subgroup of | #30628263, #30628265, #30628343, … |
| maximal quotient of | #30628294, #30628296, C4×C22⋊D491, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7856, 40);