Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C22×C42 |
| direct product | C17×#13928 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C17 | C24 |
| commutator | C23 | C23×C4×C17 |
| Frattini, cosocle | C24 | C24×C17 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
1226 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 4 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,21)(23,26)(27,29)(30,31,34,32)(33,36,37,35)(40,44)(43,45);(31,32)(35,36)(38,39,42,41)(40,45,44,43);(22,23)(24,27)(25,26)(28,29)(30,32,34,31)(33,36,37,35)(38,40,42,44)(39,43,41,45);(22,24,25,28)(23,27,26,29)(30,33)(31,35)(32,36)(34,37)(38,41,42,39)(40,45,44,43)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6916);