Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | #117×C41 ⋊ C2 |
| Sylow | C41 ⋊ #520 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D41 |
| commutator | C2×C41 | C23×C4 |
| Fitting | #117×C41 | C2 |
| socle, cosocle | C22×C41 | C24 |
| prime radical | C2×#10620306 | C2 |
| hypercenter | #117 | D41 |
| hypocenter | C41 | #520 |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ #117 | |
294 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 151 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,d^2=e,b^a=be,d^a=de,c^b=ce,g^c=g^40434 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 1029);