Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2668 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C11 · Schur multiplier (H2) = C2×C42 |
| direct product | C11×#2736 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C24×C11 |
| prime radical | C25×C11 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C11 ◁ G | |
560 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 560 conjugacy classes of subgroups — too many to draw. Only its 176 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 352 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,18)(15,16)(17,19)(20,21,24,25)(22,26,27,23)(28,29,31,33)(30,34,35,32);(13,16)(14,19)(21,25)(23,26)(28,29,31,33)(30,32,35,34);(12,14)(13,17)(15,19)(16,18)(20,22)(21,23)(24,27)(25,26)(28,29)(30,32)(31,33)(34,35);(12,13)(14,17)(15,16)(18,19)(20,23)(21,22)(24,26)(25,27)(28,30)(29,32)(31,35)(33,34)352 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 1468);