Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#22001 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C23×C17 | C23×C4 |
| prime radical | C22×D4×C17 | C2×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
780 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
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)(20,24)(21,23)(22,25)(26,27)(28,31)(29,30)(32,33)(34,35,37,41,38,40,44,47)(36,39,43,45,42,46,48,49);(18,20)(19,22)(21,25)(23,24);(20,25)(22,24)(27,30)(31,33)(34,36)(35,39)(37,43)(38,42)(40,46)(41,45)(44,48)(47,49);(19,23)(22,24)(26,28,29,32)(27,31,30,33)(35,40)(36,42)(41,47)(43,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 14989);