Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60685 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C22×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C23×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C17×#117 ◁ G | |
1878 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27)(28,33)(29,41)(30,35)(31,46)(32,36)(34,44)(37,52)(38,48)(39,49)(40,55)(42,56)(43,51)(45,57)(47,54)(50,53);(19,22)(23,25)(26,28)(27,33)(29,42)(30,39)(31,40)(32,38)(34,50)(35,49)(36,48)(37,45)(41,56)(43,54)(44,53)(46,55)(47,51)(52,57);(26,29,31,44,32,45,30,43)(27,34,35,41,36,51,46,57)(28,37,40,54,38,42,39,53)(33,47,49,52,48,50,55,56);(18,20,21,24)(19,23,22,25)(28,38)(33,48)(37,42)(39,40)(47,50)(49,55)(52,56)(53,54);(26,30,32,31)(27,35,36,46)(28,39,38,40)(29,43,45,44)(33,49,48,55)(34,41,51,57)(37,53,42,54)(47,52,50,56)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53673);