Finite Group DatabasebetaFinite Group Databasebeta| order | 24150 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C23 · Schur multiplier (H2) = C5 |
| direct product | C3×C23×C5⋊D35 |
| unambiguous semidirect product | C5⋊(C3×C23×D35) |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C23 | C5⋊D35 |
| commutator, cosocle, hypocenter | C52×C7 | C2×C3×C23 |
| Frattini | C1 | G |
| Fitting, socle | C3×C52×C7×C23 | C2 |
| LCS | G ▷ C52×C7 | |
| UCS | C1 ◁ C3×C23 | |
128 conjugacy classes of subgroups.
| transitive degree | μt(G) = 12075 |
6141 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24150, 67);