Finite Group DatabasebetaFinite Group Databasebeta| order | 312 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 4032 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C23 |
| abelian | C23×C3×C13 |
| multiplicative | (ℤ/632)ˣ, (ℤ/948)ˣ |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
64 conjugacy classes of subgroups.
| minimal degree | μ(G) = 22 |
| transitive degree | μt(G) = 312 |
A minimal faithful permutation representation — 3 generators on 22 points:
(1,2)(7,8,9)(10,11,12,13,14,15,16,17,18,19,20,21,22);(3,4);(5,6)312 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(312, 61);