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×#34369 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C2×C17×#532 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2410 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)(18,19,20,21)(23,26)(24,28)(30,31,34,35)(32,38,39,36)(33,41,42,37)(40,43,45,44);(23,26)(27,29)(31,35)(32,39)(37,41)(40,45);(22,23,25,26)(24,27,28,29)(30,31)(32,36)(33,37)(34,35)(38,39)(40,43)(41,42)(44,45);(22,24)(23,27)(25,28)(26,29)(30,32,34,39)(31,36,35,38)(33,40,42,45)(37,43,41,44);(30,33,34,42)(31,37,35,41)(32,40,39,45)(36,43,38,44)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27357);