Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2069 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C11 · Schur multiplier (H2) = C22 |
| direct product | C11×#2070 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C11 | #396 |
| commutator, Frattini, cosocle | C22×C4 | C23×C11 |
| prime radical | C23×C11 | C2×Q8 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C11 ◁ C22×C4×C11 ◁ G | |
196 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 3 generators on 43 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13,16,30,17,21,32,20)(14,22,24,18,25,38,42,34)(15,26,28,35,29,19,31,36)(23,39,40,33,27,37,41,43);(12,14,16,24,17,25,32,42)(13,18,20,22,21,34,30,38)(15,27,28,41,29,23,31,40)(19,33,35,39,26,43,36,37);(12,15,17,29)(13,19,21,26)(14,23,25,27)(16,31,32,28)(18,33,34,43)(20,36,30,35)(22,37,38,39)(24,41,42,40)253 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 802);