Finite Group DatabasebetaFinite Group Databasebeta| order | 22010 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×#24927023 |
| Fitting, socle, Hall | C2×C31×C71 ⋊ C5 |
| derived, Hall | C31×C71 ⋊ C2×C5 |
| Hall | C2×C71 ⋊ ΓL(1,𝔽32) |
| Sylow | C71 ⋊ C2×ΓL(1,𝔽32) |
| Hall | C2×C31 ⋊ C71⋊C5 |
| Sylow | C31 ⋊ C2×C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #24927023 |
| commutator, cosocle, hypocenter | C31×C71 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C31×C71 | C5 |
| LCS | G ▷ C31×C71 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4402 |
890 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(22010, 4);