Finite Group DatabasebetaFinite Group Databasebeta| order | 8604 |
| isoclinism | isoclinic class of D239 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×C32×D239 |
| unambiguous semidirect product | C239⋊(C22×C32) |
| unambiguous semidirect product | (C2×C239)⋊(C2×C32) |
| Fitting, socle | C2×C32×C239 ⋊ C2 |
| derived, Sylow | C239 ⋊ C22×C32 |
| Hall | C32×C239 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C32 | D239 |
| commutator, hypocenter | C239 | C22×C32 |
| Frattini | C1 | G |
| Fitting, socle | C2×C32×C239 | C2 |
| LCS | G ▷ C239 | |
| UCS | C1 ◁ C2×C32 | |
60 conjugacy classes of subgroups.
2178 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8604, 30);