Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×Dic269 |
| derived, Sylow | C269 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D269 |
| commutator, hypocenter | C269 | C2×C42 |
| Frattini | C22 | C22×D269 |
| Fitting | C22×C4×C269 | C2 |
| socle | C23×C269 | C22 |
| LCS | G ▷ C269 | |
| UCS | C1 ◁ C22×C4 | |
108 conjugacy classes of subgroups.
2176 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31770359, #31770364, #31770366, … |
| maximal normal subgroup of | #31770359, #31770364, #31770366, … |
| maximal quotient of | C42×Dic269, C2×#22575360, #31770451, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 95);