Finite Group DatabasebetaFinite Group Databasebeta| order | 8864 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×C4⋊#11764308 |
| unambiguous semidirect product | D277⋊(C4⋊C4) |
| Fitting | C2×C4×C277 ⋊ C4 |
| Sylow | C277 ⋊ C2×C4⋊C4 |
92 conjugacy classes of subgroups.
572 conjugacy classes — view the full character table.
| maximal subgroup of | #31800875, #31800876, #31800881, … |
| maximal normal subgroup of | #31800875, #31800876, #31800881, … |
| maximal quotient of | C2×(C2×#11764308)⋊C4, C4×C4⋊#11764308, #31800944, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8864, 224);