Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#12987 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #121 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1869 |
| prime radical | C17×#575 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ G | |
456 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)(18,19,23,30,24,31,45,60,25,28,46,47,22,29,42,57)(20,26,35,50,34,49,66,76,33,51,43,58,40,55,71,78)(21,36,39,69,38,54,70,59,37,56,44,72,41,27,52,53)(32,61,63,79,64,48,73,75,65,68,67,81,62,74,80,77);(18,20,23,43,24,34,45,71,25,33,46,35,22,40,42,66)(19,26,47,50,31,49,57,76,28,51,30,58,29,55,60,78)(21,32,44,63,38,64,52,73,37,65,39,67,41,62,70,80)(27,48,53,77,36,68,69,79,54,74,59,75,56,61,72,81);(18,21)(19,27)(20,32)(22,41)(23,44)(24,38)(25,37)(26,48)(28,54)(29,56)(30,59)(31,36)(33,65)(34,64)(35,67)(39,46)(40,62)(42,70)(43,63)(45,52)(47,53)(49,68)(50,77)(51,74)(55,61)(57,69)(58,75)(60,72)(66,80)(71,73)(76,79)(78,81)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5975);