Finite Group DatabasebetaFinite Group Databasebeta| order | 5024 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
| direct product | C2×#14578944 |
| Sylow | C157 ⋊ C2×Q16 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22⋊D157 |
| commutator | C4×C157 | C23 |
| Frattini | C4 | C22×D157 |
| Fitting | C2×Q8×C157 | C2 |
| socle | C22×C157 | D4 |
| hypercenter | C2×Q8 | D157 |
| hypocenter | C157 | C2×Q16 |
| LCS | G ▷ C4×C157 ▷ C2×C157 ▷ C157 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×Q8 | |
60 conjugacy classes of subgroups.
794 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(5024, 163);