Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#14524137 |
| derived, Sylow | C269 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11761640 |
| commutator, hypocenter | C269 | C4×C8 |
| Frattini | C22 | C2×#11761640 |
| Fitting | C2×C4×C269 | C4 |
| socle | C22×C269 | C2×C4 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C2×C4 | |
44 conjugacy classes of subgroups.
568 conjugacy classes — view the full character table.
| maximal subgroup of | C8×#14524137, #31771446, #14524137⋊C8, … |
| maximal normal subgroup of | C8×#14524137, #31771446, #14524137⋊C8, … |
| maximal quotient of | C8×#14524137, #31771446, #31771471, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 199);