Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #92213 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | #6872 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C2 | #92213 |
| commutator, hypocenter | #6872 | C4 |
| Frattini | C2×C3×C9 | C3⋊D3 |
| Fitting, cosocle | C2×#6872 | C2 |
| socle | C2×C3 | #4181 |
| prime radical | C2×H(3,𝔽3) | D9 |
| LCS | G ▷ #6872 | |
| UCS | C1 ◁ C2 | |
70 conjugacy classes of subgroups.
| transitive degree | μt(G) = 324 |
Polycyclic presentation:
2^2,3^5|a^2=b,c^3=e,e^3=g,c^a=c^2e^2g^2,d^a=d^2,e^a=e^2g^2,g^a=g^2,d^c=df,f^c=fg^2,f^d=fg60 conjugacy classes — view the full character table.
| maximal subgroup of | #14515798, #92182⋊C4, #92181⋊C4, … |
| maximal normal subgroup of | #14515798, #92182⋊C4, #92181⋊C4, … |
| maximal quotient of | #14515673, C2×#11757336 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 61);