Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
| direct product | C2×#16861597 |
| Sylow | C257 ⋊ C2×C4⋊C4 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D257 |
| commutator | C2×C257 | C22×C4 |
| Frattini | C22 | C22×D257 |
| Fitting | C22×C4×C257 | C2 |
| socle | C23×C257 | C22 |
| hypercenter | C22×C4 | D257 |
| hypocenter | C257 | C2×C4⋊C4 |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
92 conjugacy classes of subgroups.
2068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30656462, #30656588, C4×#16861597, … |
| maximal normal subgroup of | #30656462, #30656588, C4×#16861597, … |
| maximal quotient of | C2×#22551499, C4×#16861597, #30656595, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 100);