Finite Group DatabasebetaFinite Group Databasebeta| order | 2624 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C29 |
| direct product | C2×#13050209 |
| Fitting | C22×D4×C41 ⋊ C2 |
| Sylow | C41 ⋊ C2×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center | C22 | C23×D41 |
| commutator, cosocle | C2×C41 | C25 |
| Frattini | C2 | C24×D41 |
| Fitting | C22×D4×C41 | C2 |
| socle | C22×C41 | C24 |
| hypercenter | C22×D4 | D41 |
| hypocenter | C41 | C2×H(5,𝔽2) |
| LCS | G ▷ C2×C41 ▷ C41 | |
| UCS | C1 ◁ C22 ◁ C22×D4 | |
898 conjugacy classes of subgroups; only the 447 normal subgroups are shown.
This group has 898 conjugacy classes of subgroups — too many to draw. Only its 447 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 656 |
434 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2624, 1379);