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×#455 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | #120 |
| commutator, Frattini, cosocle | C2×C4 | C23×C23 |
| prime radical | C23×H(5,𝔽2) | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ G | |
152 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)(24,25,28,31)(26,32,34,39)(27,35,37,30)(29,36,38,33);(24,26)(25,29)(27,36)(28,34)(30,39)(31,38)(32,35)(33,37);(27,37)(30,35)(32,39)(33,36)368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 136);