Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| isoclinism | isoclinic class of #11758167 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2×C33 |
No aliases for this group.
| Fitting, socle, derived, Sylow | C35 ⋊ C22 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, cosocle, hypocenter | C35 | C22 |
| LCS | G ▷ C35 | |
| UCS | C1 | |
1708 conjugacy classes of subgroups.
| transitive degree | μt(G) = 108 |
Polycyclic presentation:
2^2,3^5|c^a=c^2,d^a=d^2,e^a=e^2,g^a=g^2,c^b=c^2,d^b=d^2,e^b=e^2,f^b=f^287 conjugacy classes — view the full character table.
| maximal subgroup of | D32⋊(C3⋊(C3⋊D3)), #14519522, #14519524, … |
| maximal normal subgroup of | D32⋊(C3⋊(C3⋊D3)), #14519522, #14519524, … |
| maximal quotient of | #14519441, #14519442, #14519443, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 892);