Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #61609 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#61856 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#540 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C7×#533 ◁ G | |
1612 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 5 generators on 55 points:
(1,2,3,4,5,6,7)(8,9)(10,16)(11,14)(12,15)(13,18)(17,22)(19,21)(20,23)(24,25)(26,34)(27,38)(28,32)(29,42)(30,36)(31,40)(33,41)(35,50)(37,45)(39,47)(43,46)(44,54)(48,52)(49,53)(51,55);(8,10,12,18)(9,13,15,16)(11,19,20,17)(14,22,23,21)(24,26,28,36)(25,30,32,34)(27,35,39,51)(29,37,41,53)(31,44,46,48)(33,45,42,49)(38,55,47,50)(40,52,43,54);(24,27,28,39)(25,31,32,46)(26,35,36,51)(29,43,41,40)(30,44,34,48)(33,47,42,38)(37,54,53,52)(45,50,49,55);(8,11,12,20)(9,14,15,23)(10,17,18,19)(13,21,16,22)(26,36)(30,34)(35,51)(37,53)(44,48)(45,49)(50,55)(52,54);(9,15)(13,16)(14,23)(21,22)(25,32)(26,36)(31,46)(33,42)(35,51)(37,53)(38,47)(52,54)343 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 54844);