Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #92191 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C3 · Schur multiplier (H2) = C2×C3 |
| direct product | C2×#92191 |
| Fitting | C2×#6879 ⋊ C2 |
| Sylow | #6879 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92191 |
| commutator, cosocle, hypocenter | #732 | C22×C3 |
| Frattini | C3×C9 | C2×C3×D3 |
| Fitting | C2×#6879 | C2 |
| socle | C2×C3 | #4178 |
| LCS | G ▷ #732 | |
| UCS | C1 ◁ C2 | |
80 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
62 conjugacy classes — view the full character table.
| maximal subgroup of | #92191⋊C4, #14515822, #14515824, … |
| maximal normal subgroup of | #92191⋊C4, #14515822, #14515824, … |
| maximal quotient of | #14515996, C4×#92191, C4⋊#92191, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 220);