Finite Group DatabasebetaFinite Group Databasebeta| order | 4617 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of C32⋊H(3,𝔽3) |
| automorphism | ? |
| homology | Abelianization (H1) = C33×C19 · Schur multiplier (H2) = C32 |
| direct product | C19×#6895 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C32×C19 | C33 |
| commutator, Frattini, cosocle | C32 | C33×C19 |
| prime radical | C33×C19 | C32 |
| LCS | G ▷ C32 ▷ C1 | |
| UCS | C1 ◁ C32×C19 ◁ G | |
114 conjugacy classes of subgroups.
| minimal degree | μ(G) = 55 |
| transitive degree | μt(G) = 1539 |
A minimal faithful permutation representation — 3 generators on 55 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,23,22,25,27,26,24,28)(29,30,33)(31,35,41)(32,36,40)(34,42,39)(37,44,49)(38,45,48)(43,50,47)(46,52,54)(51,55,53);(30,34,36)(33,40,42)(35,43,45)(41,48,50)(44,51,52)(49,54,55);(21,24,25)(23,27,28)(29,31,37,32,38,46,39,47,53)(30,35,44,36,45,52,34,43,51)(33,41,49,40,48,54,42,50,55)969 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4617, 42);