Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #7855 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#7864 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C42 |
| 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 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
552 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)(20,27,29,33)(21,25)(22,31)(23,26)(24,28,32,30)(34,35,38,42,39,43,37,41)(36,40,44,47,45,48,46,49);(18,20,22,30,23,29,21,28)(19,24,25,27,26,32,31,33)(34,36)(35,40)(37,46)(38,44)(39,45)(41,49)(42,47)(43,48);(34,37,39,38)(35,41,43,42)(36,44,45,46)(40,47,48,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 852);