Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #8803 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#8804 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #383 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| prime radical | C23×C17 | #126 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
216 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,27,29,31)(21,23)(22,26)(24,28,32,33)(25,30)(34,35)(36,44,46,49)(37,41,47,40)(38,42)(39,43)(45,48);(19,23,26,25)(24,27,32,31)(34,36,45,47,39,46,38,37)(35,40,42,44,43,41,48,49);(18,20,21,28,22,29,30,33)(19,24,25,31,26,32,23,27)(34,37,38,46,39,47,45,36)(35,41,42,49,43,40,48,44)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1792);