Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1902 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C7×C8 · Schur multiplier (H2) = C24 |
| direct product | C7×#9088 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C2×C4 | C22×C7×C8 |
| Frattini, cosocle | C2×C42 | C23×C7 |
| prime radical | C23×C7 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
480 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 3 generators on 47 points:
(1,2,3,4,5,6,7)(8,9,11,14,12,10,13,15)(16,17)(18,27)(19,31,34,41)(20,35)(21,25)(22,26)(23,29)(24,33,40,32)(28,43,45,37)(30,38)(36,39)(42,44,47,46);(8,10,11,15,12,9,13,14)(16,18,20,29,22,30,21,36)(17,23,25,27,26,39,35,38)(19,28,33,46,34,45,32,44)(24,37,41,42,40,43,31,47);(16,19,22,34)(17,24,26,40)(18,28,30,45)(20,33,21,32)(23,37,39,43)(25,41,35,31)(27,42,38,47)(29,46,36,44)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 2076);