Finite Group DatabasebetaFinite Group Databasebeta| order | 1792 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3198 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C7 · Schur multiplier (H2) = C24 |
| direct product | C7×#21968 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C7 | C22×D4 |
| commutator | C2×C4 | C23×C4×C7 |
| Frattini, cosocle | C22×C4 | C24×C7 |
| prime radical | C24×C7 | C2×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C7 ◁ C2×C7×#117 ◁ G | |
754 conjugacy classes of subgroups.
| minimal degree | μ(G) = 35 |
| transitive degree | μt(G) = 896 |
A minimal faithful permutation representation — 4 generators on 35 points:
(1,2,3,4,5,6,7)(8,9,10,11)(12,13)(14,18)(15,17)(16,19)(21,26)(22,29)(23,25)(27,34)(30,35)(31,32);(12,14,15,19)(13,16,17,18)(20,21,24,26)(22,30,32,27)(23,33,25,28)(29,34,31,35);(14,19)(16,18)(20,22,23,31,24,32,25,29)(21,27,33,34,26,30,28,35);(13,17)(16,18)(20,23,24,25)(21,28,26,33)(22,31,32,29)(27,35,30,34)364 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1792, 14956);