Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#13283 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C2×D8 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
390 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 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)(22,23)(24,28)(25,26)(27,29)(30,31)(32,33)(34,38)(35,45)(36,41)(37,40)(39,42)(43,44);(19,21)(23,26)(27,28)(30,32,42,41,35,43,44,45,36,39,33,31,37,38,34,40);(22,24,25,29)(23,27,26,28)(30,33,35,34,36,42,37,44)(31,38,40,32,41,43,45,39)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6271);