Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #1347 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#7274 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | #102 |
| commutator | C2×C8 | C42×C17 |
| Frattini, cosocle | C2×C4×C8 | C22×C17 |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
262 conjugacy classes of subgroups.
| minimal degree | μ(G) = 45 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 2 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)(24,26)(25,28)(27,29)(31,36)(32,40)(33,42)(34,41)(37,38)(39,45)(43,44);(23,26)(24,29)(27,28)(30,31,33,37,34,38,32,36,35,39,40,44,41,43,42,45)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 262);