Finite Group DatabasebetaFinite Group Databasebeta| order | 8608 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C2×#16864401 |
| Fitting | C2×D4×C269 ⋊ C2 |
| Sylow | C269 ⋊ C2×#41 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D269 |
| commutator | C2×C269 | C24 |
| Frattini | C2 | C23×D269 |
| Fitting | C2×D4×C269 | C2 |
| socle | C22×C269 | C23 |
| hypercenter | C2×D4 | D269 |
| hypocenter | C269 | C2×#41 |
| LCS | G ▷ C2×C269 ▷ C269 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
164 conjugacy classes of subgroups.
1360 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #31770577, #31770586, #31770598, … |
| maximal normal subgroup of | #31770577, #31770586, #31770598, … |
| maximal quotient of | C2×#22575409, C2×#22575411, C2×#22575413, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8608, 188);