Finite Group DatabasebetaFinite Group Databasebeta| order | 7856 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C491 ⋊ Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | C22⋊D491 |
| commutator | C4×C491 | C22 |
| Frattini | C4 | C2×D491 |
| Fitting | Q8×C491 | C2 |
| socle | C2×C491 | D4 |
| hypercenter | Q8 | D491 |
| hypocenter | C491 | Q16 |
| LCS | G ▷ C4×C491 ▷ C2×C491 ▷ C491 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ Q8 | |
18 conjugacy classes of subgroups.
Polycyclic presentation:
2^4,491|a^2=d,b^2=d,c^2=d,b^a=bc,c^a=cd,c^b=cd,e^b=e^4901232 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Q16×D491, C2×#21463318, #30628357, … |
| maximal normal subgroup of | Q16×D491, C2×#21463318, #30628357, … |
| maximal quotient of | #30628260, #30628261, #30628270, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7856, 30);