Finite Group DatabasebetaFinite Group Databasebeta| order | 1408 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C11 · Schur multiplier (H2) = C28 |
| direct product | C11×#3532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C11 | C25 |
| commutator, Frattini, cosocle | C22 | C25×C11 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C11 ◁ G | |
1336 conjugacy classes of subgroups.
| minimal degree | μ(G) = 27 |
| transitive degree | μt(G) = 176 |
A minimal faithful permutation representation — 5 generators on 27 points:
(1,2,3,4,5,6,7,8,9,10,11)(12,13)(14,20)(15,19)(16,18)(17,22)(21,24)(23,26)(25,27);(12,14)(13,17)(15,22)(16,21)(18,25)(19,20)(23,27)(24,26);(13,18)(14,21)(19,26)(22,27);(13,18)(14,22)(17,24)(19,26)(20,25)(21,27);(13,19)(17,20)(18,26)(24,25)418 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1408, 2264);