Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×#11764308 |
| Fitting | D4×C277 ⋊ C4 |
| Sylow | C277 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11764308 |
| commutator, socle | C2×C277 | C22×C4 |
| Fitting | D4×C277 | C4 |
| hypercenter | D4 | #11764308 |
| hypocenter | C277 | C4×D4 |
| LCS | G ▷ C2×C277 ▷ C277 | |
| UCS | C1 ◁ C2 ◁ D4 | |
94 conjugacy classes of subgroups.
365 conjugacy classes — view the full character table.
| maximal subgroup of | D8×#11764308, SD16×#11764308, #31801041, … |
| maximal normal subgroup of | D8×#11764308, SD16×#11764308, #31801041, … |
| maximal quotient of | C22⋊C4×#11764308, C4⋊C4×#11764308, #31800949, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 226);