Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C4 |
| direct product | C4×#14523339 |
| derived, Sylow | C257 ⋊ C4×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C42 | D257 |
| commutator, hypocenter | C257 | C4×C8 |
| Frattini | C2×C4 | C2×D257 |
| Fitting | C42×C257 | C2 |
| socle | C22×C257 | C2×C4 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C42 | |
44 conjugacy classes of subgroups.
2080 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#14523339, #30656458, #30656459, … |
| maximal normal subgroup of | C8×#14523339, #30656458, #30656459, … |
| maximal quotient of | C8×#14523339, #30656458, #30656492, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 55);