Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C22×C4 |
| direct product | C2×C4×Dic257 |
| derived, Sylow | C257 ⋊ C2×C42 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C4 | D257 |
| commutator, hypocenter | C257 | C2×C42 |
| Frattini | C22 | C22×D257 |
| Fitting | C22×C4×C257 | C2 |
| socle | C23×C257 | C22 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C22×C4 | |
108 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30656491, #30656496, #30656498, … |
| maximal normal subgroup of | #30656491, #30656496, #30656498, … |
| maximal quotient of | C42×Dic257, C2×#22551499, #30656583, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 95);