Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #23892 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23893 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
1610 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)(10,21)(11,27)(12,33)(13,37)(14,19)(15,20)(16,24)(17,31)(18,34)(22,50)(23,39)(25,41)(26,40)(28,48)(29,59)(30,45)(32,44)(35,47)(36,46)(38,52)(42,56)(43,62)(49,53)(51,68)(54,65)(55,64)(57,60)(58,63)(61,67)(66,71)(69,70);(8,10)(9,16)(11,28)(12,23)(13,25)(14,24)(15,26)(17,42)(18,39)(19,40)(20,41)(21,37)(22,30)(27,38)(29,58)(31,52)(32,56)(33,49)(34,55)(35,53)(36,54)(43,66)(44,50)(45,48)(46,64)(47,65)(51,61)(57,63)(59,68)(60,71)(62,70)(67,69);(8,11)(9,17)(10,22)(12,29)(13,30)(14,31)(15,32)(16,38)(18,43)(19,44)(20,45)(21,48)(23,51)(24,28)(25,56)(26,52)(27,37)(33,57)(34,60)(35,61)(36,62)(39,63)(40,42)(41,50)(46,67)(47,59)(49,68)(53,70)(54,71)(55,58)(64,66)(65,69);(8,12,15,36)(9,18,20,47)(10,23,26,54)(11,29,32,62)(13,35,14,34)(16,39,41,65)(17,43,45,59)(19,46,37,33)(21,49,40,64)(22,51,52,71)(24,55,25,53)(27,57,44,67)(28,58,56,70)(30,61,31,60)(38,63,50,69)(42,66,48,68)280 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16881);