Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #447 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#462 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C23 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ C42×C23 ◁ G | |
108 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(28,29,32,35)(30,36,38,43)(31,39,41,34)(33,40,42,37);(24,25,26,27);(28,30,32,38)(29,33,35,42)(31,40,41,37)(34,43,39,36)437 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 143);