Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1665 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C7 · Schur multiplier (H2) = C24 |
| direct product | C2×C7×#1679 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | #121 |
| commutator, Frattini, cosocle | C42 | C24×C7 |
| prime radical | C22×C7×D4 | D4 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C42×C7 ◁ G | |
758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 25 points:
(1,2)(19,20,21,22,23,24,25);(3,4,7,9)(5,10,8,6)(11,12)(13,15)(14,16)(17,18);(3,5,6,4,7,8,10,9)(12,15)(16,17);(12,16)(14,18)(15,17)406 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 12095);