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×H(5,𝔽2) |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | C24 |
| commutator, Frattini, cosocle | C2 | C24×C17 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ G | |
166 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 136 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,22)(23,25);(19,22)(23,24);(18,19)(20,23)(21,22)(24,25);(18,20)(19,23)(21,25)(22,24)289 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(544, 240);