Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C2×C7×#3490 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
9502 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 6 generators on 25 points:
(1,2)(19,20,21,22,23,24,25);(3,4)(5,11)(6,10)(7,9)(8,12)(13,17)(14,16)(15,18);(3,5,7,13)(4,8,9,15)(6,12,14,18)(10,11,16,17);(4,9)(8,15)(10,16)(11,17);(5,12)(8,11)(13,18)(15,17);(4,10)(8,11)(9,16)(15,17)616 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55754);