Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×#11761640 |
| unambiguous semidirect product | D269⋊C42 |
| Fitting | C2×C4×C269 ⋊ C4 |
| derived, Sylow | C269 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11761640 |
| commutator, hypocenter | C269 | C2×C42 |
| Frattini | C2 | C22×#11761640 |
| Fitting | C2×C4×C269 | C4 |
| socle | C22×C269 | C2×C4 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C2×C4 | |
108 conjugacy classes of subgroups.
568 conjugacy classes — view the full character table.
| maximal subgroup of | (C2×#11761640)⋊C8, #31771475, #31771477, … |
| maximal normal subgroup of | (C2×#11761640)⋊C8, #31771475, #31771477, … |
| maximal quotient of | C42×#11761640, C2×(C2×#11761640)⋊C4, #31771541, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 222);