Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C7×#23421 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C7 | C2×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C23×C7 | C22×D4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C7 ◁ C22×C42×C7 ◁ G | |
2094 conjugacy classes of subgroups.
| minimal degree | μ(G) = 31 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 31 points:
(1,2,3,4,5,6,7)(8,9)(10,11)(16,17)(18,27)(19,24)(20,25)(21,26)(22,29)(23,28)(30,31);(9,11)(12,13)(14,15)(16,18)(17,22)(19,28)(20,29)(21,30)(23,26)(24,27)(25,31);(13,15)(16,18)(17,23)(19,28)(20,29)(21,30)(22,26)(24,31)(25,27);(16,19,21,20)(17,24,26,25)(18,28,30,29)(22,27,23,31)448 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16409);