Finite Group DatabasebetaFinite Group Databasebeta| order | 544 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(5,𝔽2) |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×2−1+4 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C24 |
| commutator, Frattini, cosocle | C2 | C24×C17 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ G | |
146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 272 |
A minimal faithful permutation representation — 4 generators on 33 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,23)(21,29)(24,26)(27,33);(18,19,22,23)(20,26,28,24)(21,25,29,30)(27,32,33,31);(18,20,22,28)(19,24,23,26)(21,27,29,33)(25,31,30,32);(18,21)(19,25)(20,27)(22,29)(23,30)(24,31)(26,32)(28,33)289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 241);