Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | #95×C41 ⋊ C2 |
| Sylow | C41 ⋊ #385 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D41 |
| commutator | C22×C41 | C22×C4 |
| Fitting | #95×C41 | C2 |
| socle, cosocle | C23×C41 | C23 |
| prime radical | C23×D41 | C22 |
| hypercenter | #95 | D41 |
| hypocenter | C41 | #385 |
| LCS | G ▷ C22×C41 ▷ C41 | |
| UCS | C1 ◁ C23 ◁ #95 | |
234 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 1312 |
Polycyclic presentation:
2^6,41|a^2=f,b^2=f,b^a=bd,c^a=ce,g^a=g^40,g^c=g^40428 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 423);