Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #6875 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C92 · Schur multiplier (H2) = C32 |
| direct product | C2×#10624472 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C32 | C9⋊C9 |
| commutator | C9 | C2×C92 |
| Frattini, cosocle | C32×C9 | C2×C32 |
| prime radical | C2×C33 | 3−1+2 |
| LCS | G ▷ C9 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C32 ◁ C2×C32×C9 ◁ G | |
170 conjugacy classes of subgroups.
| transitive degree | μt(G) = 162 |
210 conjugacy classes — view the full character table.
| Fitting subgroup of | C2×#10624472⋊C2 |
| maximal subgroup of | C2×C9×#6875, C2×#14550484, C2×#14550487, … |
| maximal normal subgroup of | C2×C9×#6875, C2×#14550484, C2×#14550487, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 32);