Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C2×C7×#3255 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G | |
1866 conjugacy classes of subgroups.
| minimal degree | μ(G) = 33 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 33 points:
(1,2)(27,28,29,30,31,32,33);(4,7)(5,9)(11,12,16,19)(13,17,15,24)(14,21,23,25)(18,22,26,20);(3,4)(5,8)(6,7)(9,10)(11,13,16,15)(12,17,19,24)(14,22,23,20)(18,21,26,25);(4,7)(8,10)(11,14,16,23)(12,18,19,26)(13,20,15,22)(17,25,24,21);(3,5,6,9)(4,8,7,10)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53893);