Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #92208 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| derived, Sylow | #6867 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92208 |
| commutator, hypocenter | #6867 | C4 |
| Frattini, prime radical | C2×C33 | C3⋊D3 |
| Fitting, cosocle | C2×#6867 | C2 |
| socle | C2×C32 | #272 |
| LCS | G ▷ #6867 | |
| UCS | C1 ◁ C2 | |
96 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^2,3^5|a^2=b,c^3=e,d^3=g,c^a=c^2e^2,d^a=d^2g^2,e^a=e^2,f^a=fg^2,g^a=g^2,d^c=df,f^c=fg60 conjugacy classes — view the full character table.
| maximal subgroup of | #92175⋊C4, #92176⋊C4, #14515781, … |
| maximal normal subgroup of | #92175⋊C4, #92176⋊C4, #14515781, … |
| maximal quotient of | #14515668, C2×#11757331 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 56);