Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C2×C4 |
No aliases for this group.
| Fitting | #97×C41 ⋊ C2 |
| Sylow | C41 ⋊ #496 |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C2×D164 |
| commutator, cosocle | C2×C4×C41 | C23 |
| Frattini | C2×C4 | C22×D41 |
| Fitting | #97×C41 | C2 |
| socle | C22×C41 | C2×D4 |
| hypercenter | #97 | D41 |
| hypocenter | C41 | #496 |
| LCS | G ▷ C2×C4×C41 ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C42 ◁ #97 | |
144 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1312 |
Polycyclic presentation:
2^6,41|b^2=d,c^2=e,d^2=f,b^a=bd,c^a=ce,d^a=df,g^a=g^40,c^b=cf416 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 938);