Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3192 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C7 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×C7×#3217 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C7 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C22×C42×C7 ◁ G | |
2834 conjugacy classes of subgroups.
| minimal degree | μ(G) = 25 |
| transitive degree | μt(G) = 448 |
A minimal faithful permutation representation — 5 generators on 25 points:
(1,2)(19,20,21,22,23,24,25);(3,4)(5,9)(6,8)(7,10)(11,12)(13,15)(14,16)(17,18);(3,5,6,10)(4,7,8,9)(12,15)(16,17);(5,10)(7,9)(12,16)(14,18)(15,17);(4,8)(7,9)(12,15)(16,17)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 53773);