Finite Group DatabasebetaFinite Group Databasebeta| order | 28055 |
| automorphism | ? |
| homology | Abelianization (H1) = C5×C181 · Schur multiplier (H2) = C1 |
| direct product | ΓL(1,𝔽32)×C181 |
| unambiguous semidirect product | C31⋊(C5×C181) |
| Fitting, socle, Hall | C31×C181 ⋊ C5 |
| derived, Sylow | C31 ⋊ C5×C181 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C181 | ΓL(1,𝔽32) |
| commutator, cosocle, hypocenter | C31 | C5×C181 |
| Frattini | C1 | G |
| Fitting, socle | C31×C181 | C5 |
| LCS | G ▷ C31 | |
| UCS | C1 ◁ C181 | |
8 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5611 |
1991 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(28055, 1);