Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #62842 |
| automorphism | ? |
| homology | Abelianization (H1) = C26×C17 · Schur multiplier (H2) = C214 |
| direct product | C17×#62859 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C26 |
| commutator, Frattini, cosocle | C22 | C26×C17 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ G | |
10986 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 6 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(23,29)(24,30)(27,41)(31,38)(33,43)(36,49)(39,51)(48,53);(18,19)(20,21)(22,23,28,29)(24,25,30,37)(26,38,40,31)(27,32,41,42)(33,46,43,35)(34,36,44,49)(39,50,51,45)(47,53,52,48);(22,24)(23,25)(26,33)(27,34)(28,30)(29,37)(31,35)(32,36)(38,46)(39,47)(40,43)(41,44)(42,49)(45,48)(50,53)(51,52);(22,25)(23,30)(24,29)(26,35)(27,36)(28,37)(31,43)(32,44)(33,38)(34,42)(39,48)(40,46)(41,49)(45,52)(47,50)(51,53);(22,26,28,40)(23,31,29,38)(24,33,30,43)(25,35,37,46)(27,39,41,51)(32,45,42,50)(34,47,44,52)(36,48,49,53);(22,27)(23,32)(24,34)(25,36)(26,39)(28,41)(29,42)(30,44)(31,45)(33,47)(35,48)(37,49)(38,50)(40,51)(43,52)(46,53)1394 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 55847);