Finite Group DatabasebetaFinite Group Databasebeta| order | 1472 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #560 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C23 · Schur multiplier (H2) = C24 |
| direct product | C23×#564 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C23 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C23 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C23 ◁ G | |
172 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1472 |
A minimal faithful permutation representation — 4 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)(26,32)(27,35)(29,33)(30,37)(40,41,44,47)(42,45,50,48)(43,51,52,46)(49,54,55,53);(24,25,28,31)(26,33,32,29)(27,30,35,37)(34,39,38,36)(40,41)(42,48)(43,51)(44,47)(45,50)(46,52)(49,53)(54,55);(24,26,28,32)(25,29,31,33)(27,34,35,38)(30,36,37,39)(40,42)(41,45)(43,49)(44,50)(46,53)(47,48)(51,54)(52,55);(24,27)(25,30)(26,34)(28,35)(29,36)(31,37)(32,38)(33,39)(40,43,44,52)(41,46,47,51)(42,49,50,55)(45,53,48,54)437 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1472, 245);