Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
| direct product | C2×C22⋊Dic269 |
| Sylow | C269 ⋊ C2×C22⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D269 |
| commutator | C2×C269 | C22×C4 |
| Frattini | C22 | C22×D269 |
| Fitting | C24×C269 | C2 |
| socle | C23×C269 | C22 |
| hypercenter | C24 | D269 |
| hypocenter | C269 | C2×C22⋊C4 |
| LCS | G ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C23 ◁ C24 | |
132 conjugacy classes of subgroups.
2164 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31770371, #31770372, C4×C22⋊Dic269, … |
| maximal normal subgroup of | #31770371, #31770372, C4×C22⋊Dic269, … |
| maximal quotient of | C2×#22575360, C4×C22⋊Dic269, #31770461, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 98);