Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60460 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C28 |
| direct product | C7×#60727 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C4×C7×#41 ◁ G | |
1902 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,13)(11,12)(14,15)(16,17)(18,26)(19,29)(20,23)(21,24)(22,27)(25,31)(28,30);(9,12)(13,15)(16,18,21,20)(17,23,24,26)(19,25,30,27)(22,28,31,29);(16,19,22,23,21,30,31,26)(17,20,25,29,24,18,27,28);(8,10,11,14)(9,13,12,15)(16,20,21,18)(17,23,24,26)(19,25,30,27)(22,29,31,28);(18,20)(19,30)(23,26)(28,29)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53715);