Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1414 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C11 · Schur multiplier (H2) = C2 |
| direct product | C11×#1414 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #354 |
| commutator | C42 | C2×C4×C11 |
| Frattini, cosocle | #124 | C22×C11 |
| prime radical | C2×D4×C11 | D4 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C11 ◁ C2×C4×C11 ◁ C11×#124 ◁ G | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 2 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,22,24,37)(15,26,28,42)(16,30,32,20)(17,21)(18,23,33,40)(19,29)(25,39,31,38)(27,34,41,35)(36,43);(12,14)(13,18,21,35)(15,27)(16,31)(17,25)(19,22,36,39)(20,33,30,34)(23,28)(24,32)(26,37,42,38)(29,41)(40,43)187 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 146);