Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C42×C17 · Schur multiplier (H2) = C23×C4 |
| direct product | C17×#20563 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C24 |
| commutator | C22 | C22×C42×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C23×C17 | C23×C4 |
| prime radical | C22×D4×C17 | C2×C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ G | |
954 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 2176 |
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)(22,23)(24,28)(25,27)(26,29)(30,31,34,33,35,37,43,42)(32,36,40,41,39,44,45,38);(18,19,20,21)(22,24)(23,26)(25,29)(27,28)(30,32)(31,36)(33,41)(34,40)(35,39)(37,44)(38,42)(43,45);(24,29)(26,28)(30,33,34,37,35,42,43,31)(32,38,40,36,39,41,45,44);(23,27)(26,28)(32,39)(36,44)(38,41)(40,45)1292 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13551);