Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60756 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60927 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3062 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
1772 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)(19,22)(20,24)(26,27)(28,36)(29,40)(30,34)(31,45)(32,38)(33,43)(35,44)(37,53)(39,48)(41,57)(42,51)(46,50)(47,56)(49,54)(52,55);(18,19)(20,23)(21,22)(24,25)(26,28)(27,32)(29,41)(30,38)(31,39)(33,49)(34,36)(35,48)(37,42)(40,53)(43,56)(44,55)(45,52)(46,54)(47,50)(51,57);(19,22)(23,25)(26,29,30,42)(27,33,34,50)(28,37,38,41)(31,46,44,43)(32,47,36,49)(35,51,45,40)(39,56,55,54)(48,53,52,57);(18,20,21,24)(19,23,22,25)(27,34)(32,36)(33,50)(35,45)(40,51)(47,49)(48,52)(53,57);(28,38)(32,36)(37,41)(39,55)(47,49)(48,52)(53,57)(54,56)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53915);