Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C41 ⋊ #407 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×#4223 |
| commutator, socle | C22×C41 | C22×C4 |
| Fitting, prime radical | C24×C41 | C4 |
| cosocle | C2×Dic41 | C23 |
| hypercenter | C24 | #4223 |
| hypocenter | C41 | #407 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C24 | |
190 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^6,41|a^2=e,e^2=f,b^a=bd,c^a=cf,g^a=g^32,g^e=g^40188 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 1519);