Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| isoclinism | isoclinic class of #4223 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C16 · Schur multiplier (H2) = C23 |
| direct product | C2×#13050237 |
| derived, Sylow | C41 ⋊ C22×C16 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2×C8 | #4223 |
| commutator, hypocenter | C41 | C22×C16 |
| Frattini | C4 | C22×#4223 |
| Fitting | C2×C8×C41 | C4 |
| socle | C22×C41 | C2×C8 |
| prime radical | C22×D41 | C8 |
| cosocle | #66491 | C23 |
| LCS | G ▷ C41 | |
| UCS | C1 ◁ C2×C8 | |
98 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1312 |
224 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 1603);