Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61488 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#529 ◁ G | |
1788 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)(28,37)(29,41)(30,35)(31,36)(32,45)(33,40)(34,42)(38,53)(39,49)(43,50)(44,48)(46,51)(47,54)(52,56)(55,57);(18,19)(20,23)(21,22)(24,25)(26,28)(27,33)(29,38)(30,44)(31,40)(32,39)(34,47)(35,49)(36,37)(41,57)(42,56)(43,55)(45,48)(46,54)(50,53)(51,52);(26,29,31,43)(27,34,36,51)(28,38,40,55)(30,42,32,46)(33,47,37,52)(35,50,45,41)(39,54,44,56)(48,57,49,53);(19,22)(23,25)(26,30,31,32)(27,35,36,45)(28,39,40,44)(29,42,43,46)(33,48,37,49)(34,50,51,41)(38,54,55,56)(47,57,52,53);(18,20,21,24)(19,23,22,25)(28,40)(33,37)(38,55)(39,44)(47,52)(48,49)(53,57)(54,56)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54476);