Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C2×C35 |
| direct product | A4×#737 |
| Fitting | C22×#737 ⋊ C3 |
| Sylow | C22 ⋊ C3×#737 |
| subgroup | G/H | |
|---|---|---|
| center | C9 | C32×A4 |
| commutator, socle, cosocle | C22×C3 | C34 |
| Frattini | C3 | C33×A4 |
| Fitting | C22×#737 | C3 |
| prime radical | A4×H(3,𝔽3) | C3 |
| hypercenter | #737 | A4 |
| hypocenter | C22 | C3×#737 |
| LCS | G ▷ C22×C3 ▷ C22 | |
| UCS | C1 ◁ C9 ◁ #737 | |
513 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
132 conjugacy classes — view the full character table.
| maximal subgroup of | S4×#737, A4⋊#4208, A4⋊#4207, … |
| maximal normal subgroup of | S4×#737, A4⋊#4208, A4⋊#4207, … |
| maximal quotient of | SL(2,𝔽3)×#737, C2×A4×#737, #72228707, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 830);