Finite Group DatabasebetaFinite Group Databasebeta| order | 8776 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4 · Schur multiplier (H2) = C2 |
| direct product | C2×#17984203 |
| unambiguous semidirect product | D1097⋊C4 |
| Fitting, socle | C2×C1097 ⋊ C4 |
| derived, Sylow | C1097 ⋊ C2×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #17984203 |
| commutator, hypocenter | C1097 | C2×C4 |
| Frattini | C1 | G |
| Fitting, socle | C2×C1097 | C4 |
| LCS | G ▷ C1097 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
556 conjugacy classes — view the full character table.
| maximal subgroup of | C4×#17984203, C22⋊#17984203, C4⋊#17984203, … |
| maximal normal subgroup of | C4×#17984203, C22⋊#17984203, C4⋊#17984203, … |
| maximal quotient of | C4×#17984203, C22⋊#17984203, C4⋊#17984203, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8776, 14);