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×#34189 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | C25 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C23 | C25×C17 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ G | |
2342 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)(24,28)(26,29)(30,31)(32,36)(33,40)(34,35)(37,41)(38,44)(39,42)(43,45);(22,23,25,27)(24,26,28,29)(31,35)(36,42)(37,40)(43,44);(22,24,25,28)(23,26,27,29)(30,32,34,39)(31,36,35,42)(33,38,41,45)(37,43,40,44);(30,31)(32,36)(33,37)(34,35)(38,43)(39,42)(40,41)(44,45);(30,33,34,41)(31,37,35,40)(32,38,39,45)(36,43,42,44)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 27177);