Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #120 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#126 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23 |
| commutator, Frattini, cosocle | C22 | C23×C17 |
| prime radical | C23×C17 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
60 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 3 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(20,27)(25,32)(26,30)(28,31)(29,33);(18,19,24,30)(20,25,31,32)(21,23,22,26)(27,33,28,29);(18,20,21,28)(19,25,23,29)(22,27,24,31)(26,33,30,32)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 188);