Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2002 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C26 |
| direct product | C2×C7×#2040 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #120 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C2×C7×#537 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C23×C4×C7 ◁ G | |
1498 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 4 generators on 29 points:
(1,2)(23,24,25,26,27,28,29);(4,5)(7,8)(9,17)(10,15)(11,14)(12,16)(13,19)(18,22)(20,21);(3,4)(5,6)(7,9)(8,13)(10,19)(11,20)(12,18)(14,22)(15,17)(16,21);(3,5,6,4)(8,14)(9,18)(11,12)(15,16)(19,20)(21,22)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16485);