Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | D16×C41 ⋊ C2 |
| Sylow | C41 ⋊ #509 |
| subgroup | G/H | |
|---|---|---|
| center | C2 | D8×D41 |
| commutator, cosocle | C8×C41 | C23 |
| Frattini | C8 | C22×D41 |
| Fitting | D16×C41 | C2 |
| socle | C2×C41 | C2×D8 |
| hypercenter | D16 | D41 |
| hypocenter | C41 | #509 |
| LCS | G ▷ C8×C41 ▷ C4×C41 ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C2 ◁ C4 ◁ C8 ◁ D16 | |
90 conjugacy classes of subgroups.
| transitive degree | μt(G) = 656 |
Polycyclic presentation:
2^6,41|d^2=ef,e^2=f,b^a=bd,c^a=cf,d^a=de,e^a=ef,d^b=de,e^b=ef,g^c=g^40236 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 983);