Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | D4×#11759967 |
| Fitting | D4×C257 ⋊ C4 |
| Sylow | C257 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×#11759967 |
| commutator, socle | C2×C257 | C22×C4 |
| Fitting | D4×C257 | C4 |
| hypercenter | D4 | #11759967 |
| hypocenter | C257 | C4×D4 |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C2 ◁ D4 | |
94 conjugacy classes of subgroups.
340 conjugacy classes — view the full character table.
| maximal subgroup of | D8×#11759967, SD16×#11759967, #30657776, … |
| maximal normal subgroup of | D8×#11759967, SD16×#11759967, #30657776, … |
| maximal quotient of | C22⋊C4×#11759967, C4⋊C4×#11759967, #30657684, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 226);