Finite Group DatabasebetaFinite Group Databasebeta| order | 7816 |
| automorphism | ? |
| homology | Abelianization (H1) = C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C977 ⋊ C8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C977 | C8 |
| LCS | G ▷ C977 | |
| UCS | C1 | |
8 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,977|a^2=b,b^2=c,d^a=d^439,d^b=d^252,d^c=d^976130 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#21463100, #30627621 |
| maximal normal subgroup of | C2×#21463100, #30627621 |
| maximal quotient of | #30627619, C2×#21463100 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7816, 15);