Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| derived, Sylow | #6879 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, socle, hypercenter | C2×C3 | #4185 |
| commutator, hypocenter | #6879 | C4 |
| Frattini | C2×C3×C9 | C3⋊D3 |
| Fitting, prime radical, cosocle | C2×#6879 | C2 |
| LCS | G ▷ #6879 | |
| UCS | C1 ◁ C2×C3 | |
68 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3^5|a^2=b,e^3=g^2,c^a=c^2,d^a=d^2,f^a=f^2g,d^c=de,e^c=ef,f^c=fg,e^d=ef^2g,f^d=fg^262 conjugacy classes — view the full character table.
| maximal subgroup of | #14515819, #92191⋊C4, #92192⋊C4, … |
| maximal normal subgroup of | #14515819, #92191⋊C4, #92192⋊C4, … |
| maximal quotient of | #14515676, C2×#11757339 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 64);