Finite Group DatabasebetaFinite Group Databasebeta| order | 29110 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C5 · Schur multiplier (H2) = C1 |
| direct product | C2×#28410023 |
| Fitting, socle, Hall | C2×C41×C71 ⋊ C5 |
| derived, Hall | C41×C71 ⋊ C2×C5 |
| Hall | C2×C71 ⋊ C41⋊C5 |
| Hall | C2×C41 ⋊ C71⋊C5 |
| Sylow | C71 ⋊ C2×C41⋊C5 |
| Sylow | C41 ⋊ C2×C71⋊C5 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #28410023 |
| commutator, cosocle, hypocenter | C41×C71 | C2×C5 |
| Frattini | C1 | G |
| Fitting, socle | C2×C41×C71 | C5 |
| LCS | G ▷ C41×C71 | |
| UCS | C1 ◁ C2 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 5822 |
1174 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(29110, 5);