Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13101 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1898 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C2×C17×2−1+4 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C17×2−1+4 ◁ G | |
630 conjugacy classes of subgroups.
| minimal degree | μ(G) = 81 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 81 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,24,30,25,31,23,29)(20,32,37,62,38,63,36,61)(21,39,42,27,43,55,41,56)(22,44,33,59,47,28,48,50)(26,49,52,45,53,71,58,35)(34,65,68,60,69,80,67,77)(40,74,64,54,46,73,75,57)(51,70,78,81,79,66,72,76);(18,20,33,49)(19,26,50,62)(21,34,64,76)(22,45,24,36)(23,37,47,35)(25,38,48,71)(27,51,73,65)(28,32,30,52)(29,58,44,63)(31,53,59,61)(39,72,57,60)(40,70,42,67)(41,68,46,66)(43,69,75,81)(54,77,55,78)(56,79,74,80);(18,21,25,43)(19,27,31,56)(20,34,38,69)(22,46,47,40)(23,42,24,41)(26,51,53,79)(28,57,44,54)(29,55,30,39)(32,60,63,77)(33,64,48,75)(35,70,45,66)(36,68,37,67)(49,76,71,81)(50,73,59,74)(52,72,58,78)(61,80,62,65)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6089);