Finite Group DatabasebetaFinite Group Databasebeta| order | 2528 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
| direct product | C2×D632 |
| Fitting | C2×C8×C79 ⋊ C2 |
| Sylow | C79 ⋊ C2×D8 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | D316 |
| commutator, cosocle | C4×C79 | C23 |
| Frattini | C4 | C22×D79 |
| Fitting | C2×C8×C79 | C2 |
| socle | C22×C79 | D4 |
| hypercenter | C2×C8 | D79 |
| hypocenter | C79 | C2×D8 |
| LCS | G ▷ C4×C79 ▷ C2×C79 ▷ C79 | |
| UCS | C1 ◁ C22 ◁ C2×C4 ◁ C2×C8 | |
76 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1264 |
638 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2528, 157);