Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C42×C8×C17 · Schur multiplier (H2) = C2×C42 |
| direct product | C4×C17×#346 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C8×C17 | C22 |
| commutator | C2 | C42×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle, prime radical | C23×C17 | C22×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C8×C17 ◁ G | |
510 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(9,10,11,15,12,16,17,22,13,14,18,20,19,21,23,24);(5,6,7,8)(10,14)(15,20)(16,21)(22,24)2720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5526);