Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
| direct product | C23×Dic269 |
| derived, Sylow | C269 ⋊ C23×C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C24 | D269 |
| commutator, hypocenter | C269 | C23×C4 |
| Frattini | C2 | C23×D269 |
| Fitting, socle | C24×C269 | C2 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C24 | |
236 conjugacy classes of subgroups.
2176 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×#22575360, C22⋊C4×Dic269, #31770463, … |
| maximal normal subgroup of | C2×#22575360, C22⋊C4×Dic269, #31770463, … |
| maximal quotient of | C22×C4×Dic269, C22×C22⋊Dic269, C22×C4⋊Dic269, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 181);