Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C23 |
| direct product | C23×#456 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #120 |
| commutator, Frattini, cosocle | C2×C4 | C23×C23 |
| prime radical | C23×2−1+4 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ G | |
142 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 368 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,29,27)(26,32,35,39)(28,36,38,31)(30,37,33,34);(24,26)(25,30)(27,33)(28,37)(29,35)(31,39)(32,36)(34,38);(24,27,29,25)(26,33,35,30)(28,31,38,36)(32,37,39,34)368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 137);