Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #453 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12685 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #120 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1779 |
| prime radical | C17×#585 | C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ 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)(18,19,23,29,24,30,44,57,25,31,45,58,22,28,42,55)(20,32,36,60,34,48,66,56,35,53,43,71,40,26,46,49)(21,27,38,51,37,50,67,76,39,52,69,78,41,54,70,79)(33,61,64,81,65,47,73,75,63,59,68,80,62,74,72,77);(18,20)(19,26)(21,33)(22,40)(23,43)(24,34)(25,35)(27,47)(28,53)(29,56)(30,32)(31,48)(36,45)(37,65)(38,68)(39,63)(41,62)(42,66)(44,46)(49,58)(50,59)(51,77)(52,74)(54,61)(55,60)(57,71)(64,69)(67,72)(70,73)(75,78)(76,81)(79,80);(18,21)(19,27)(20,33)(22,41)(23,38)(24,37)(25,39)(26,47)(28,54)(29,51)(30,50)(31,52)(32,59)(34,65)(35,63)(36,64)(40,62)(42,70)(43,68)(44,67)(45,69)(46,72)(48,74)(49,75)(53,61)(55,79)(56,77)(57,76)(58,78)(60,80)(66,73)(71,81)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5673);