Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17547 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17617 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3506 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×D4×C17 ◁ G | |
1018 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,26,28,23)(21,24)(22,25)(27,32,33,30)(29,31)(34,35)(36,43)(37,41)(38,46)(39,42)(40,44)(45,48)(47,49);(18,20)(19,23)(21,27)(22,28)(24,30)(25,26)(29,33)(31,32)(34,36)(35,40)(37,44)(38,47)(39,45)(41,48)(42,49)(43,46);(18,21)(19,24)(20,27)(22,29)(23,30)(25,31)(26,32)(28,33)(34,37,39,38)(35,41,42,46)(36,44,45,47)(40,48,49,43);(21,29)(24,31)(27,33)(30,32)(34,37,39,38)(35,41,42,46)(36,44,45,47)(40,48,49,43)1037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10605);