Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3532 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C7 · Schur multiplier (H2) = C213 |
| direct product | C2×C7×#3532 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
9542 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)(8,13)(12,15)(14,17)(16,18);(3,5)(4,8)(6,13)(7,12)(9,16)(10,11)(14,18)(15,17);(4,9)(5,12)(10,17)(13,18);(4,9)(5,13)(8,15)(10,17)(11,16)(12,18);(4,10)(8,11)(9,17)(15,16)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55706);