Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C29 |
| direct product | C11×#3489 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
1522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,21,22)(18,24,26,19)(20,28,29,23)(25,27,31,30);(17,22)(19,24)(23,28)(27,30);(12,13)(14,15)(16,18)(17,19)(20,25)(21,26)(22,24)(23,27)(28,30)(29,31);(16,19)(17,18)(20,27)(21,24)(22,26)(23,25)(28,31)(29,30);(16,20,21,29)(17,23,22,28)(18,25,26,31)(19,27,24,30)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2221);