Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×Q8×C41 ⋊ C2 |
| Sylow | C41 ⋊ #550 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D41 |
| commutator, socle, cosocle | C22×C41 | C24 |
| Fitting | C4×Q8×C41 | C2 |
| hypercenter | C4×Q8 | D41 |
| hypocenter | C41 | #550 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C4×Q8 | |
312 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1312 |
Polycyclic presentation:
2^6,41|b^2=e,c^2=e,d^2=e,b^a=be,c^a=cf,g^a=g^40,d^b=de,g^c=g^40425 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 1221);