Finite Group DatabasebetaFinite Group Databasebeta| order | 2598 |
| isoclinism | isoclinic class of C433⋊C3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3 · Schur multiplier (H2) = C1 |
| direct product | C2×C433⋊C3 |
| unambiguous semidirect product | (C2×C433)⋊C3 |
| Fitting, socle, Hall | C2×C433 ⋊ C3 |
| derived, Sylow | C433 ⋊ C2×C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | C433⋊C3 |
| commutator, cosocle, hypocenter | C433 | C2×C3 |
| Frattini | C1 | G |
| Fitting, socle | C2×C433 | C3 |
| LCS | G ▷ C433 | |
| UCS | C1 ◁ C2 | |
8 conjugacy classes of subgroups.
| minimal degree | μ(G) = 435 |
| transitive degree | μt(G) = 866 |
294 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C2×C5×C433⋊C3, D5×C433⋊C3, C2×C7×C433⋊C3, … |
| maximal normal subgroup of | C2×C5×C433⋊C3, C2×C7×C433⋊C3, C2×C11×C433⋊C3, … |
| maximal quotient of | C2×C5×C433⋊C3, D5×C433⋊C3, C2×C7×C433⋊C3, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(2598, 2);