Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C23 |
| direct product | C2×#16861626 |
| derived, Sylow | C257 ⋊ C22×C8 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C4 | #11759967 |
| commutator, hypocenter | C257 | C22×C8 |
| Frattini | C2 | C22×#11759967 |
| Fitting | C2×C4×C257 | C4 |
| socle | C22×C257 | C2×C4 |
| LCS | G ▷ C257 | |
| UCS | C1 ◁ C2×C4 | |
76 conjugacy classes of subgroups.
544 conjugacy classes — view the full character table.
| maximal subgroup of | #30657602, #30657610, #30657612, … |
| maximal normal subgroup of | #30657602, #30657610, #30657612, … |
| maximal quotient of | C2×C4×#14523346, C4×#16861626, #30657705, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 229);