Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1655 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#1658 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | #120 |
| commutator, Frattini, cosocle | C42 | C23×C11 |
| prime radical | C11×#127 | C22 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ C42×C11 ◁ G | |
182 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 704 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,18)(14,21)(15,16)(20,23)(22,24)(25,26)(29,33)(31,38)(34,42)(35,39)(36,40)(41,43);(12,13)(14,19)(15,23)(16,18)(17,20)(21,26)(22,27)(24,25)(28,29,32,35)(30,34,37,43)(31,39,38,33)(36,41,40,42);(12,14,17,22)(13,19,20,27)(15,21,16,24)(18,25,23,26)(28,30,32,37)(29,34,35,43)(31,40,38,36)(33,41,39,42)220 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 390);