Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | H(5,𝔽3) ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, socle, hypercenter | C3 | C3⋊(C3⋊#157) |
| commutator, Fitting, hypocenter | H(5,𝔽3) | C4 |
| prime radical, cosocle | #92392 | C2 |
| LCS | G ▷ H(5,𝔽3) | |
| UCS | C1 ◁ C3 | |
153 conjugacy classes of subgroups.
| transitive degree | μt(G) = 54 |
Polycyclic presentation:
2^2,3^5|a^2=b,c^a=cd,d^a=cd^2g^2,e^a=e^2,f^a=f^2,c^b=c^2,d^b=d^2g,d^c=dg,f^e=fg^238 conjugacy classes — view the full character table.
| maximal subgroup of | #14519099, #14519129, #14519160, … |
| maximal normal subgroup of | #14519099, #14519129, #14519160, … |
| maximal quotient of | #14518599, C2×#11758049 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 774);