Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C22×C42 |
| direct product | C7×#22056 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#447 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
1136 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,11,10)(12,13)(14,18)(15,17)(16,19)(20,21,24,28)(22,25,29,33)(23,26,31,27)(30,32,35,34);(8,10,11,9)(12,14)(13,16)(15,19)(17,18)(20,22)(21,25)(23,30)(24,29)(26,32)(27,34)(28,33)(31,35);(14,19)(16,18)(21,26)(23,31)(25,32)(27,28)(30,35)(33,34);(13,17)(16,18)(22,29)(25,33)(30,35)(32,34)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 15044);