Finite Group DatabasebetaFinite Group Databasebeta| order | 972 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C3 |
No aliases for this group.
| Fitting, derived, Sylow | #6855 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C3 | #66343 |
| commutator, Fitting, hypocenter | #6855 | C4 |
| Frattini, socle | C33 | #157 |
| prime radical, cosocle | #92197 | C2 |
| LCS | G ▷ #6855 | |
| UCS | C1 ◁ C3 | |
61 conjugacy classes of subgroups.
| transitive degree | μt(G) = 36 |
Polycyclic presentation:
2^2,3^5|a^2=b,c^3=e,d^3=f,c^a=cdf^2,d^a=cd^2f^2g^2,e^a=ef,f^a=ef^2,c^b=c^2e^2,d^b=d^2f^2g,e^b=e^2,f^b=f^2,d^c=dg36 conjugacy classes — view the full character table.
| maximal subgroup of | #14516408, #11757369⋊C2, #14516413, … |
| maximal normal subgroup of | #14516408, #11757369⋊C2, #14516413, … |
| maximal quotient of | #14515710, C2×#11757369 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(972, 94);