Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C8 |
| direct product | C17×#8270 |
| subgroup | G/H | |
|---|---|---|
| center | C42×C17 | C2×D4 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | C4×C4⋊C4 |
| prime radical | C23×C17 | #117 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
342 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)(19,23,25,28)(24,30,31,32)(34,35)(36,39)(37,41)(38,40)(42,46)(43,45)(44,47)(48,49);(18,19)(20,24)(21,28)(22,25)(23,29)(26,32)(27,31)(30,33)(34,36,37,42,38,43,44,48)(35,39,41,46,40,45,47,49);(18,20,21,26,22,27,29,33)(19,24,28,32,25,31,23,30)(35,40)(39,45)(41,47)(46,49)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1258);