Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13396 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#13397 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #2034 |
| commutator, Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
390 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)(18,19,25,31)(20,26,35,51)(21,36,38,70)(22,42,46,58)(23,30,24,29)(27,52,54,39)(28,44,59,45)(32,61,62,81)(33,64,67,80)(34,60,47,50)(37,72,68,69)(40,71,41,57)(43,56,74,55)(48,76,77,63)(49,75,78,66)(53,73,79,65);(18,20)(19,26)(21,37)(22,33)(23,47)(24,34)(25,35)(27,53)(28,49)(29,60)(30,50)(31,51)(32,40)(36,69)(38,68)(39,73)(41,62)(42,64)(43,63)(44,75)(45,66)(46,67)(48,55)(52,65)(54,79)(56,77)(57,61)(58,80)(59,78)(70,72)(71,81)(74,76);(18,21,24,40,25,38,23,41)(19,27,30,55,31,54,29,56)(20,32,34,68,35,62,47,37)(22,43,45,52,46,74,44,39)(26,48,50,79,51,77,60,53)(28,57,42,70,59,71,58,36)(33,65,66,76,67,73,75,63)(49,72,64,81,78,69,80,61)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6385);