Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #11115 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#11314 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | #388 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| socle | C2×C7 | #1443 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C23×C4×C7 ◁ G | |
548 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 224 |
A minimal faithful permutation representation — 3 generators on 39 points:
(1,2,3,4,5,6,7)(8,9,13,18,14,17,12,19)(10,20,22,31,24,15,23,32)(11,25,28,34,29,35,27,16)(21,33,26,36,37,39,38,30);(8,10,12,22,14,24,13,23)(9,15,19,32,17,20,18,31)(11,26,27,37,29,38,28,21)(16,33,35,36,34,39,25,30);(8,11)(9,16,17,34)(10,21)(12,27)(13,28)(14,29)(15,30,20,36)(18,25,19,35)(22,26)(23,38)(24,37)(31,39,32,33)322 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 4302);