Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #9996 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C7 · Schur multiplier (H2) = C23 |
| direct product | C7×#10003 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #392 |
| commutator, Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | #120 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
500 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,16)(10,17,19,22)(11,15,12,20)(14,21,23,18)(24,25)(26,32)(27,35)(28,31)(29,34)(30,37)(33,39)(36,38);(8,10,13,19)(9,14,16,23)(11,18,12,21)(15,22,20,17)(29,38)(32,39);(8,11,13,12)(9,15,16,20)(10,18,19,21)(14,22,23,17)(24,26)(25,29)(27,36)(28,33)(30,39)(31,38)(32,35)(34,37)259 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2991);