Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#34254 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C24×C17 | C24 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2234 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 45 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,20)(24,28)(26,29)(30,31,35,33)(32,36,40,38)(34,41,42,37)(39,44,45,43);(22,23,25,27)(24,26,28,29)(31,33)(36,38)(37,41)(43,44);(18,20,21,19)(22,24)(23,26)(25,28)(27,29)(30,32,35,40)(31,36,33,38)(34,39,42,45)(37,43,41,44);(30,33,35,31)(32,38,40,36)(34,41,42,37)(39,44,45,43);(30,34,35,42)(31,37,33,41)(32,39,40,45)(36,43,38,44)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27242);