Finite Group DatabasebetaFinite Group Databasebeta| order | 24045 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C5 · Schur multiplier (H2) = C1 |
| direct product | C5×#18012479 |
| Fitting, socle, Hall | C5×C7×C229 ⋊ C3 |
| derived, Hall | C7×C229 ⋊ C3×C5 |
| Hall | C5×C229 ⋊ ΓL(1,𝔽8) |
| Sylow | C229 ⋊ C5×ΓL(1,𝔽8) |
| Hall | C5×C7 ⋊ C229⋊C3 |
| Sylow | C7 ⋊ C5×C229⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C5 | #18012479 |
| commutator, cosocle, hypocenter | C7×C229 | C3×C5 |
| Frattini | C1 | G |
| Fitting, socle | C5×C7×C229 | C3 |
| LCS | G ▷ C7×C229 | |
| UCS | C1 ◁ C5 | |
16 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8015 |
2685 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24045, 5);