Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61544 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3518 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#529 ◁ G | |
1754 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
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)(19,22)(23,25)(26,27,32,36)(28,33,40,49)(29,42,44,51)(30,37,31,35)(34,45,50,43)(38,52,54,57)(39,48,41,47)(46,55,56,53);(18,19)(20,23)(21,22)(24,25)(26,28)(27,33)(29,38)(30,39)(31,41)(32,40)(34,46)(35,47)(36,49)(37,48)(42,52)(43,53)(44,54)(45,55)(50,56)(51,57);(26,29,32,44)(27,34,36,50)(28,38,40,54)(30,43,31,45)(33,46,49,56)(35,42,37,51)(39,53,41,55)(47,52,48,57);(19,22)(23,25)(26,30,32,31)(27,35,36,37)(28,39,40,41)(29,43,44,45)(33,47,49,48)(34,42,50,51)(38,53,54,55)(46,52,56,57);(18,20,21,24)(19,23,22,25)(27,36)(28,40)(34,50)(35,37)(38,54)(39,41)(42,51)(53,55)935 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54532);