Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2021 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C27 |
| direct product | C2×C7×#2022 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #120 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| prime radical | C2×C7×#534 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C25×C7 ◁ G | |
2394 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);(3,4)(5,6)(7,8)(9,12)(10,13)(11,14)(15,18)(16,19)(17,21)(20,22);(7,9,11,16)(8,12,14,19)(10,15,17,22)(13,20,21,18);(4,6)(7,10)(8,13)(9,15)(11,17)(12,18)(14,21)(16,22)(19,20)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 16430);