Finite Group DatabasebetaFinite Group Databasebeta| order | 8224 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
| direct product | C22×Dic514 |
| Sylow | C257 ⋊ C22×Q8 |
| subgroup | G/H | |
|---|---|---|
| center | C23 | C2×D257 |
| commutator | C2×C257 | C24 |
| Frattini | C2 | C23×D257 |
| Fitting | C22×C4×C257 | C2 |
| socle | C23×C257 | C22 |
| hypercenter | C22×C4 | D257 |
| hypocenter | C257 | C22×Q8 |
| LCS | G ▷ C2×C257 ▷ C257 | |
| UCS | C1 ◁ C23 ◁ C22×C4 | |
156 conjugacy classes of subgroups.
2068 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #30656641, #30656642, #30656643, … |
| maximal normal subgroup of | #30656641, #30656642, #30656643, … |
| maximal quotient of | C22×#16861597, C22×C4⋊Dic257, C2×C4×Dic514, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(8224, 186);