Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #10624760 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C35 |
| direct product | C2×#10624761 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C32⋊H(3,𝔽3) |
| commutator, Frattini, cosocle | C33 | C2×C33 |
| LCS | G ▷ C33 ▷ C3 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C33 ◁ G | |
476 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 54 |
114 conjugacy classes — view the full character table.
| Fitting subgroup of | #72228150, #72228151, C2×#13091158, … |
| maximal subgroup of | #72228150, C2×#14554854, C2×#14554344, … |
| maximal normal subgroup of | #72228150, C2×#14554854, C2×#14554344, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 321);