Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #509 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C23 · Schur multiplier (H2) = C22 |
| direct product | C23×#510 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C23 | C2×D8 |
| commutator, Frattini, cosocle | C8 | C23×C23 |
| prime radical | C23×#135 | C2 |
| LCS | G ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C23 ◁ C2×C4×C23 ◁ C2×C8×C23 ◁ G | |
82 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 736 |
A minimal faithful permutation representation — 3 generators on 55 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)(26,34)(27,38)(28,43)(29,31)(30,35)(32,41)(33,40)(36,54)(37,51)(39,49)(42,50)(44,48)(45,53)(46,55)(47,52);(24,26,29,37)(25,30,31,45)(27,39,42,55)(28,44,40,36)(32,48,47,54)(33,49,43,46)(34,50,51,38)(35,52,53,41);(25,31)(30,45)(32,47)(33,43)(34,51)(38,50)(46,49)(48,54)368 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 191);