Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C22×Q8×C41 ⋊ C2 |
| Sylow | C41 ⋊ #393 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D41 |
| commutator, socle, cosocle | C23×C41 | C23 |
| Fitting | C22×Q8×C41 | C2 |
| prime radical | C23×D41 | C22 |
| hypercenter | C22×Q8 | D41 |
| hypocenter | C41 | #393 |
| LCS | G ▷ C23×C41 ▷ C41 | |
| UCS | C1 ◁ C23 ◁ C22×Q8 | |
202 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1312 |
Polycyclic presentation:
2^6,41|a^2=d,b^2=d,b^a=bd,c^a=ce,c^b=cf,g^c=g^40422 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 460);