Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #25196 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C25 |
| direct product | C7×#25197 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2424 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
968 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,17,14,18,12,26)(10,19,21,15,22,30,27,31)(11,23,24,33,25,32,28,16)(20,35,37,39,38,29,36,34);(8,10,13,21,14,22,12,27)(9,15,17,30,18,31,26,19)(11,20,24,37,25,38,28,36)(16,29,23,34,33,35,32,39);(8,11)(9,16)(10,20)(12,24)(13,28)(14,25)(15,29)(17,32)(18,33)(19,34)(21,36)(22,38)(23,26)(27,37)(30,39)(31,35);(8,9,14,18)(10,15,22,31)(11,16,25,33)(12,26,13,17)(19,21,30,27)(20,29,38,35)(23,28,32,24)(34,36,39,37)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 18185);