Finite Group DatabasebetaFinite Group Databasebeta| order | 1216 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D42 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C19 · Schur multiplier (H2) = C25 |
| direct product | C19×#546 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C19 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C19 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C19 ◁ G | |
334 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 304 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(21,23)(24,25,28,29)(26,30,31,27);(25,29)(27,30);(20,21)(22,23)(24,26)(25,27)(28,31)(29,30);(24,27)(25,26)(28,30)(29,31)475 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1216, 227);