Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #11669 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12745 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #418 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1786 |
| prime radical | C17×#3584 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
890 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)(20,30)(21,35,37,26)(22,39)(23,45)(24,28)(25,32)(27,43)(29,42)(31,56,59,77)(33,57)(34,63)(36,66,41,74)(38,51,68,65)(40,55)(44,71)(46,52)(47,58,64,61)(48,73)(49,62)(50,69,53,75)(54,76)(60,79,70,81)(67,78,72,80);(18,20)(19,25)(21,31)(22,40)(23,46)(24,33)(26,47)(27,52)(28,49)(29,55)(30,39)(32,43)(34,42)(35,64)(36,67)(37,59)(38,70)(41,72)(44,73)(45,48)(50,79)(51,80)(53,81)(54,63)(56,66)(57,71)(58,69)(60,68)(61,75)(62,76)(65,78)(74,77);(18,21)(19,26)(20,31)(22,41)(23,38)(24,37)(25,47)(27,53)(28,35)(29,51)(30,56)(32,61)(33,59)(34,60)(36,44)(39,66)(40,72)(42,68)(43,75)(45,65)(46,70)(48,78)(49,64)(50,54)(52,81)(55,80)(57,77)(58,62)(63,79)(67,73)(69,76)(71,74)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5733);