Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60249 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C24×C4 |
| prime radical | C24×C17 | C22×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ G | |
1702 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 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)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33)(34,35,37,41,38,40,44,47)(36,39,43,46,42,45,48,49);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36)(35,39)(37,43)(38,42)(40,45)(41,46)(44,48)(47,49);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32);(19,25)(23,26)(24,33)(31,32)(36,42)(39,45)(43,48)(46,49);(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, 53237);