Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1426 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#7476 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #367 |
| commutator | C16 | C42×C17 |
| Frattini, cosocle | C22×C16 | C22×C17 |
| socle | C2×C17 | #1380 |
| prime radical | C23×C17 | Q32 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C22×C8×C17 ◁ C22×C16×C17 ◁ G | |
162 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 2 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,22,29,26,32,25,51)(20,33,35,65,38,67,44,66)(21,30,40,60,43,63,42,77)(23,46,45,62,41,28,48,59)(24,49,39,61,47,58,50,31)(27,52,53,34,57,69,56,71)(36,74,72,55,70,64,78,80)(37,76,73,54,75,79,68,81);(18,20,23,36,47,75,40,52,22,44,45,78,50,73,43,71,26,38,41,70,24,37,42,69,25,35,48,72,39,68,21,34)(19,27,30,54,61,80,59,66,51,53,77,79,49,74,28,33,32,57,63,81,31,55,62,65,29,56,60,76,58,64,46,67)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 464);