Finite Group DatabasebetaFinite Group Databasebeta| order | 1458 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C33 · Schur multiplier (H2) = C33 |
| direct product | C3×#92281 |
| Fitting, Sylow | C3×#6909 ⋊ C2 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32 | C3×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C2×C33 |
| Frattini | C32 | C33×D3 |
| Fitting | C3×#6909 | C2 |
| hypercenter | C33 | (C3⋊D3)⋊C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C32 ◁ C33 | |
551 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 551 conjugacy classes of subgroups — too many to draw. Only its 94 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 81 |
102 conjugacy classes — view the full character table.
| maximal subgroup of | #72221974, #72243622, C3×#13091645, … |
| maximal normal subgroup of | #72221974, #72243622, C3×#13091645, … |
| maximal quotient of | #72221881, C2×C3×#92281 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1458, 1690);