Finite Group DatabasebetaFinite Group Databasebeta| order | 24102 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32×C13 · Schur multiplier (H2) = C3 |
| direct product | C3×C13×D103⋊C3 |
| unambiguous semidirect product | D103⋊(C32×C13) |
| unambiguous semidirect product | (C103⋊C3)⋊(C2×C3×C13) |
| unambiguous semidirect product | (C3×D103)⋊(C3×C13) |
| Fitting, socle | C3×C13×C103 ⋊ C2×C3 |
| derived, Sylow | C103 ⋊ C2×C32×C13 |
| Hall | C3×C13×C103⋊C3 ⋊ C2 |
| Hall | C13×D103 ⋊ C32 |
| Hall | C13×C103 ⋊ C2×C32 |
| Hall | C3×C103⋊C3 ⋊ C2×C13 |
| Hall | D103 ⋊ C32×C13 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3×C13 | D103⋊C3 |
| commutator, cosocle, hypocenter | C103 | C2×C32×C13 |
| Frattini | C1 | G |
| Fitting, socle | C3×C13×C103 | C2×C3 |
| LCS | G ▷ C103 | |
| UCS | C1 ◁ C3×C13 | |
48 conjugacy classes of subgroups.
| transitive degree | μt(G) = 4017 |
897 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(24102, 30);