Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊#11761640 |
| unambiguous semidirect product | D269⋊(C22⋊C4) |
| unambiguous semidirect product | (C2×#11761640)⋊C22 |
| Fitting | C23×C269 ⋊ C4 |
| Sylow | C269 ⋊ C2×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×#11761640 |
| commutator | C2×C269 | C22×C4 |
| Frattini | C2 | C22×#11761640 |
| Fitting | C23×C269 | C4 |
| socle | C22×C269 | C2×C4 |
| hypercenter | C23 | #11761640 |
| hypocenter | C269 | C2×C22⋊C4 |
| LCS | G ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C22 ◁ C23 | |
132 conjugacy classes of subgroups.
556 conjugacy classes — view the full character table.
| maximal subgroup of | #31771482, #31771483, C4×C22⋊#11761640, … |
| maximal normal subgroup of | #31771482, #31771483, C4×C22⋊#11761640, … |
| maximal quotient of | C2×(C2×#11761640)⋊C4, C4×C22⋊#11761640, #31771546, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 223);