Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C4×D1028 |
| Fitting | C42×C257 ⋊ C2 |
| Sylow | C257 ⋊ C4×D4 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C2×D257 |
| commutator | C2×C257 | C22×C4 |
| Frattini | C22 | C22×D257 |
| Fitting | C42×C257 | C2 |
| socle | C22×C257 | C23 |
| hypercenter | C42 | D257 |
| hypocenter | C257 | C4×D4 |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C2×C4 ◁ C42 | |
94 conjugacy classes of subgroups.
2068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30656464, #30656466, #30656802, … |
| maximal normal subgroup of | #30656464, #30656466, #30656802, … |
| maximal quotient of | C4×#16861595, C4×C4⋊Dic257, #30656611, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 110);