Finite Group DatabasebetaFinite Group Databasebeta| order | 396 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 2880 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C3 |
| abelian | C22×C32×C11 |
| multiplicative | (ℤ/469)ˣ, (ℤ/603)ˣ, (ℤ/938)ˣ, (ℤ/1206)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 21 |
| transitive degree | μt(G) = 396 |
A minimal faithful permutation representation — 2 generators on 21 points:
(1,2)(5,6,7)(11,12,13,14,15,16,17,18,19,20,21);(3,4)(8,9,10)396 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(396, 30);