Finite Group DatabasebetaFinite Group Databasebeta| order | 108 |
| nilpotency class | 1 |
| isoclinism | isoclinic class of C1 |
| automorphism | Aut(G) order 67392 |
| homology | Abelianization (H1) = G · Schur multiplier (H2) = C2×C33 |
| abelian | C22×C33 |
| subgroup | G/H | |
|---|---|---|
| center | G | C1 |
| commutator, Frattini | C1 | G |
| LCS | G ▷ C1 | |
| UCS | C1 ◁ G | |
140 conjugacy classes of subgroups.
| minimal degree | μ(G) = 13 |
| transitive degree | μt(G) = 108 |
A minimal faithful permutation representation — 3 generators on 13 points:
(1,2)(5,6,7);(3,4)(8,9,10);(11,12,13)108 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(108, 45);