Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of UT(4,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C35 |
| direct product | C2×#10624750 |
| 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 | |
414 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 92 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 83 |
| transitive degree | μt(G) = 162 |
114 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 310);