Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×Q8×C41 ⋊ C4 |
| Sylow | C41 ⋊ #519 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C23×#4223 |
| commutator, socle | C2×C41 | C23×C4 |
| Fitting | C2×Q8×C41 | C4 |
| prime radical | C22×D41 | C23 |
| cosocle | C2×D41 | C24 |
| hypercenter | C2×Q8 | #4223 |
| hypocenter | C41 | #519 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C2 ◁ C2×Q8 | |
266 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^6,41|a^2=f,b^2=e,c^2=e,b^a=be,d^a=de,g^a=g^32,c^b=ce,g^f=g^40134 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 1617);