Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#7986 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #95 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | C2×#95 |
| prime radical | C24×C17 | C4⋊C4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C22×C42×C17 ◁ G | |
546 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,25,23,27,22,26)(20,28,29,24,31,32,30,33)(34,35,38,43,39,42,37,41)(36,44,45,49,46,40,47,48);(18,20,22,30,23,31,21,29)(19,24,25,32,27,33,26,28)(34,36)(35,40)(37,45)(38,47)(39,46)(41,48)(42,44)(43,49);(18,21,23,22)(19,25,27,26)(20,29,31,30)(24,32,33,28)(34,37,39,38)(35,41,42,43)(36,45,46,47)(40,48,44,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 974);