Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6875 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C3×C27 · Schur multiplier (H2) = C3 |
| direct product | C2×#10624462 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C2×C32 | C9⋊C9 |
| commutator | C9 | C2×C3×C27 |
| Frattini, cosocle | C92 | C2×C32 |
| LCS | G ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C92 ◁ G | |
72 conjugacy classes of subgroups.
| transitive degree | μt(G) = 1458 |
210 conjugacy classes — view the full character table.
| Fitting subgroup of | C2×#10624462⋊C2 |
| maximal subgroup of | C2×#10624462⋊C2, C2×#14546335 |
| maximal normal subgroup of | C2×#10624462⋊C2, C2×#14546335 |
| maximal quotient of | C2×#14546335 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 22);