Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C42 |
| direct product | C17×#8138 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C42 |
| commutator | C4 | C2×C4×C8×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #376 |
| prime radical | C23×C17 | #117 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ G | |
354 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 3 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,21,23,20,22,24,25)(26,27)(28,36,39,49)(29,33)(30,34)(31,35)(32,38,44,52)(37,48,51,56)(40,45)(41,46)(42,47)(43,50,54,57)(53,55);(19,22)(23,25)(26,28)(27,32,35,44)(29,37)(30,38)(31,39)(33,43,46,54)(34,36,47,49)(40,50)(41,51)(42,52)(45,48,55,56)(53,57);(26,29,30,40,31,41,42,53)(27,33,34,45,35,46,47,55)(28,37,38,50,39,51,52,57)(32,43,36,48,44,54,49,56)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 1126);