Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60768 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60879 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| prime radical | C7×#535 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
1654 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 448 |
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)(26,30)(27,32)(28,31)(29,34)(33,40)(35,42)(36,41)(37,44)(38,46)(39,45)(43,50)(47,51)(48,53)(49,52)(54,55);(8,10,12,18)(9,13,15,16)(11,19,20,17)(14,22,23,21)(24,26,29,37)(25,30,34,44)(27,35,38,48)(28,36,40,50)(31,41,33,43)(32,42,46,53)(39,49,51,55)(45,52,47,54);(8,11,12,20)(9,14,15,23)(10,17,18,19)(13,21,16,22)(25,31)(28,40)(30,41)(32,45)(33,34)(36,50)(39,51)(42,52)(43,44)(46,47)(49,55)(53,54);(9,15)(13,16)(14,23)(21,22)(24,27)(25,32)(26,35)(28,39)(29,38)(30,42)(31,45)(33,47)(34,46)(36,49)(37,48)(40,51)(41,52)(43,54)(44,53)(50,55);(27,38)(32,46)(35,48)(39,51)(42,53)(45,47)(49,55)(52,54)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53867);