Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C32 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#92281 |
| Fitting | C2×#6909 ⋊ C2 |
| Sylow | #6909 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | C3×(C3⋊D3)⋊C3 |
| commutator, cosocle, hypocenter | H(3,𝔽3) | C22×C32 |
| Frattini | C32 | C2×C32×D3 |
| Fitting | C2×#6909 | C2 |
| hypercenter | C2×C32 | (C3⋊D3)⋊C3 |
| LCS | G ▷ H(3,𝔽3) | |
| UCS | C1 ◁ C2×C3 ◁ C2×C32 | |
210 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 48 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| transitive degree | μt(G) = 54 |
68 conjugacy classes — view the full character table.
| maximal subgroup of | #92281⋊C4, #10619549⋊C3, #10619550⋊C3, … |
| maximal normal subgroup of | #92281⋊C4, #10619549⋊C3, #10619550⋊C3, … |
| maximal quotient of | #14517379, C4×#92281, C4⋊#92281, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 627);