Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C43×C17 · Schur multiplier (H2) = C42 |
| direct product | C17×#12542 |
| subgroup | G/H | |
|---|---|---|
| center | C16×C17 | C42 |
| commutator | C4 | C43×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1726 |
| prime radical | C23×C17 | #131 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C16×C17 ◁ G | |
350 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)(18,19,22,27,23,28,38,49,24,29,39,50,40,51,62,73)(20,25,31,42,33,44,55,66,32,43,54,65,56,67,75,79)(21,26,35,46,37,48,60,71,36,47,59,70,61,72,77,81)(30,41,52,63,34,45,57,68,53,64,74,78,58,69,76,80);(18,20)(19,25)(21,34,36,58)(22,31)(23,33)(24,32)(26,45,47,69)(27,42)(28,44)(29,43)(30,37,53,61)(35,57,59,76)(38,55)(39,54)(40,56)(41,48,64,72)(46,68,70,80)(49,66)(50,65)(51,67)(52,60,74,77)(62,75)(63,71,78,81)(73,79);(18,21)(19,26)(20,30,32,53)(22,35)(23,37)(24,36)(25,41,43,64)(27,46)(28,48)(29,47)(31,52,54,74)(33,34,56,58)(38,60)(39,59)(40,61)(42,63,65,78)(44,45,67,69)(49,71)(50,70)(51,72)(55,57,75,76)(62,77)(66,68,79,80)(73,81)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5530);