Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C34 · Schur multiplier (H2) = C34 |
| direct product | C2×#10624872 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C3×C9 | C33 |
| commutator, Frattini, cosocle | C32 | C2×C34 |
| socle | C2×C32 | C34 |
| prime radical | C2×C34 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C2×C3×C9 ◁ G | |
824 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
306 conjugacy classes. The character table is too large to display.
| Fitting subgroup of | C2×#13091435, C2×#13091433 |
| maximal subgroup of | C2×#14555333, C2×#14550738, C2×#13091435, … |
| maximal normal subgroup of | C2×#14555333, C2×#14550738, C2×#13091435, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 432);