Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C22×D4×C17 |
| unambiguous semidirect product | C4⋊(C23×C17) |
| unambiguous semidirect product | C22⋊(C23×C17) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C22 |
| commutator, Frattini, cosocle | C2 | C24×C17 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
236 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25);(3,4);(5,6,7,8);(6,8)340 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 237);