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×#3548 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C25 |
| commutator, Frattini, cosocle | C22 | C26×C7 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ G | |
7810 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 6 generators on 25 points:
(1,2)(19,20,21,22,23,24,25);(3,4)(5,7)(6,9)(8,10)(12,15)(13,17);(4,5)(8,9)(12,15)(16,18);(3,4,7,5)(6,8,10,9)(11,12,14,15)(13,16,17,18);(3,5,7,4)(6,9,10,8)(11,13)(12,16)(14,17)(15,18);(3,6,7,10)(4,8,5,9)532 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 55744);