Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61411 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1838 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)(19,23)(24,25)(26,27)(28,33)(29,40)(30,35)(31,44)(32,36)(34,41)(37,52)(38,47)(39,49)(42,50)(43,48)(45,51)(46,54)(53,56)(55,57);(18,19,22,23)(20,24,21,25)(26,28,32,39)(27,33,36,49)(29,37,42,55)(30,43,31,38)(34,46,51,56)(35,48,44,47)(40,52,50,57)(41,54,45,53);(18,20,22,21)(19,24,23,25)(26,29)(27,34)(28,37)(30,41)(31,45)(32,42)(33,46)(35,50)(36,51)(38,53)(39,55)(40,44)(43,54)(47,52)(48,57)(49,56);(18,21,22,20)(19,24,23,25);(26,30,32,31)(27,35,36,44)(28,38,39,43)(29,41,42,45)(33,47,49,48)(34,50,51,40)(37,53,55,54)(46,52,56,57)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54399);