Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62862 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C17 · Schur multiplier (H2) = C213 |
| direct product | C17×#62867 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
6758 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 6 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28)(21,26)(22,24)(23,27)(25,30)(29,38)(31,42)(32,41)(33,36)(34,37)(35,43)(39,45)(40,47)(44,49)(46,48);(19,24)(20,29)(21,32)(26,40)(27,37)(30,43)(31,46)(33,47)(36,41)(39,42)(44,45)(48,49);(18,20)(19,25)(21,31)(22,29)(23,30)(24,35)(26,39)(27,28)(32,45)(33,44)(34,43)(36,48)(37,38)(40,49)(41,42)(46,47);(19,24)(20,30)(25,38)(26,36)(27,37)(28,35)(29,43)(31,45)(39,49)(40,41)(42,48)(44,46);(18,21,22,33)(19,26,24,36)(20,31,29,44)(23,32,34,47)(25,39,35,48)(27,41,37,40)(28,42,38,49)(30,45,43,46);(19,27)(24,37)(25,28)(26,41)(35,38)(36,40)(39,42)(48,49)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55855);