Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 5 |
| isoclinism | isoclinic class of #1426 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8×C17 · Schur multiplier (H2) = C2 |
| direct product | C17×#7463 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C22×C17 | #367 |
| commutator | C16 | C2×C8×C17 |
| Frattini, cosocle | C4×C16 | C22×C17 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C42×C17 ◁ C4×C8×C17 ◁ C4×C16×C17 ◁ G | |
84 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 2 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,20,22,21,23,24,25)(27,32,34,45)(28,37)(29,41)(30,42)(33,48)(35,49,52,57)(36,55,53,47)(38,43)(39,51)(40,50)(44,56,54,46);(26,27,33,49,29,35,28,32,42,53,37,46,38,44,48,55,31,34,51,57,43,52,40,45,30,36,50,56,41,54,39,47)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 451);