Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #33691 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#33693 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #3109 |
| commutator, Frattini, cosocle | C2×C8 | C24×C7 |
| prime radical | C7×#575 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C7×#405 ◁ G | |
512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 71 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 71 points:
(1,2,3,4,5,6,7)(8,9,14,19)(10,15,21,37)(11,24,26,59)(12,29,32,64)(13,35,33,18)(16,40,42,27)(17,44,47,34)(20,48,50,58)(22,53,30,63)(23,56,52,39)(25,46,28,62)(31,41,60,43)(36,61,68,51)(38,66,45,55)(49,71,57,69)(54,70,65,67);(8,10,14,21)(9,15,19,37)(11,20,26,50)(12,30,32,22)(13,23,33,52)(16,36,42,68)(17,45,47,38)(18,39,35,56)(24,58,59,48)(25,57,28,49)(27,61,40,51)(29,63,64,53)(31,65,60,54)(34,66,44,55)(41,70,43,67)(46,71,62,69);(8,11)(9,16)(10,20)(12,31)(13,25)(14,26)(15,36)(17,46)(18,41)(19,42)(21,50)(22,54)(23,57)(24,29)(27,34)(28,33)(30,65)(32,60)(35,43)(37,68)(38,69)(39,70)(40,44)(45,71)(47,62)(48,53)(49,52)(51,55)(56,67)(58,63)(59,64)(61,66);(10,21)(11,25,26,28)(12,32)(15,37)(16,41,42,43)(17,47)(20,49,50,57)(23,52)(24,46,59,62)(27,31,40,60)(29,64)(34,44)(36,67,68,70)(39,56)(48,71,58,69)(51,65,61,54)238 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 26681);