Finite Group DatabasebetaFinite Group Databasebeta| order | 8604 |
| automorphism | Aut(G) order 6143256 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
| dihedral | D4302 |
| direct product | C2×D2151 |
| unambiguous semidirect product | (C2×C9)⋊D239 |
| unambiguous semidirect product | (C2×C239)⋊D9 |
| Fitting | C2×C9×C239 ⋊ C2 |
| derived, Hall | C9×C239 ⋊ C22 |
| Sylow | C239 ⋊ C2×D9 |
| Sylow | C9 ⋊ C2×D239 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | D2151 |
| commutator, hypocenter | C9×C239 | C22 |
| Frattini | C3 | C2×D717 |
| Fitting | C2×C9×C239 | C2 |
| socle | C2×C3×C239 | D3 |
| LCS | G ▷ C9×C239 | |
| UCS | C1 ◁ C2 | |
30 conjugacy classes of subgroups.
2154 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D8604, C2×D6453, C2×D15057 |
| maximal normal subgroup of | D8604 |
| maximal quotient of | D8604, Dic4302, C2×D6453, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8604, 8);