Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12028 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13184 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#106 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C23×C17 | C2×SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ C2×C4×C8×C17 ◁ G | |
294 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 53 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(22,23)(24,32,34,48)(25,36)(26,29)(27,41)(28,33,43,49)(30,39)(31,40)(35,50,42,46)(37,44,52,47)(38,51)(45,53);(22,24,27,42,26,34,40,35)(23,28,31,47,29,43,41,44)(25,37,39,33,38,52,53,49)(30,46,36,32,45,50,51,48);(18,19,20,21)(23,29)(28,43)(30,45)(31,41)(32,48)(36,51)(44,47)(46,50)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6172);