Finite Group DatabasebetaFinite Group Databasebeta| order | 28395 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C631 ⋊ C3×C5 |
| derived, Sylow | C631 ⋊ C32×C5 |
| Hall | C3×C631⋊C3 ⋊ C5 |
| Hall | C631⋊C5 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C631⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C631 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C631 | C3×C5 |
| LCS | G ▷ C631 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1893 |
171 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28395, 7);