Finite Group DatabasebetaFinite Group Databasebeta| order | 24345 |
| automorphism | ? |
| homology | Abelianization (H1) = C32×C5 · Schur multiplier (H2) = C3 |
| Fitting, socle | C3×C541 ⋊ C3×C5 |
| derived, Sylow | C541 ⋊ C32×C5 |
| Hall | C3×C541⋊C3 ⋊ C5 |
| Hall | C541⋊C5 ⋊ C32 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | (C541⋊C3)⋊C5 |
| commutator, cosocle, hypocenter | C541 | C32×C5 |
| Frattini | C1 | G |
| Fitting, socle | C3×C541 | C3×C5 |
| LCS | G ▷ C541 | |
| UCS | C1 ◁ C3 | |
24 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1623 |
153 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24345, 7);