Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C34 · Schur multiplier (H2) = C2×C35 |
No aliases for this group.
| Fitting | C22×#737 ⋊ C3 |
| Sylow | C22 ⋊ 3−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C3 | C33×A4 |
| commutator, socle, cosocle | C22×C3 | C34 |
| Fitting | C22×#737 | C3 |
| prime radical | A4×H(3,𝔽3) | C3 |
| hypercenter | #737 | A4 |
| hypocenter | C22 | 3−1+4 |
| LCS | G ▷ C22×C3 ▷ C22 | |
| UCS | C1 ◁ C3 ◁ #737 | |
493 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
3^5,2^2|d^3=e,d^a=de,f^a=fg,g^a=f,c^b=ce116 conjugacy classes — view the full character table.
| maximal subgroup of | #4207⋊A4, #14519263, C2×#11758106, … |
| maximal normal subgroup of | #4207⋊A4, #14519263, C2×#11758106, … |
| maximal quotient of | #14518868, C2×#11758106, #72259463, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 831);