Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #534 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#3455 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C11 | C24 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| socle | C22×C11 | C25 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C11 ◁ G | |
1040 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 5 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,16)(15,17)(18,19)(20,21)(22,28)(23,27)(24,26)(25,29)(30,34)(31,33)(32,35);(12,14,15,18)(13,16,17,19)(20,22)(21,25)(23,30)(24,29)(26,28)(27,32)(31,35)(33,34);(13,17)(16,19)(22,29)(25,28)(30,35)(32,34);(21,26)(25,28)(27,33)(32,34);(20,23,24,31)(21,27,26,33)(22,30,29,35)(25,32,28,34)484 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2187);