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×#62869 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
6510 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(20,24)(21,28)(22,23)(25,29)(26,30)(27,33)(31,32)(34,35)(36,44)(37,42)(38,43)(39,40)(41,47)(45,49)(46,48);(20,26)(24,30)(27,32)(31,33)(35,40)(41,44)(42,43)(48,49);(19,23)(24,30)(25,28)(31,33)(34,35)(36,41)(37,42)(38,43)(39,40)(44,47)(45,48)(46,49);(18,19)(20,24)(21,25)(22,23)(26,30)(27,31)(28,29)(32,33)(34,36)(35,41)(37,45)(38,46)(39,47)(40,44)(42,48)(43,49);(18,20)(19,24)(21,27)(22,26)(23,30)(25,31)(28,33)(29,32)(34,37,39,38)(35,42,40,43)(36,45,47,46)(41,48,44,49);(18,21)(19,25)(20,27)(22,29)(23,28)(24,31)(26,32)(30,33)(34,38,39,37)(35,43,40,42)(36,46,47,45)(41,49,44,48)1190 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55857);