Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#9669 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #121 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #390 |
| prime radical | C23×C17 | C4×D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
446 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 2176 |
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)(18,19,21,24,22,20,23,25)(26,27)(28,32,37,46)(29,39)(30,43)(31,34)(33,41)(35,40)(36,48,50,57)(38,52,49,45)(42,53)(44,55,56,51)(47,54);(18,20,21,25,22,19,23,24)(26,28,31,37)(27,32)(29,36,42,50)(30,38,40,49)(33,44)(34,46)(35,45)(39,48)(41,51,54,55)(43,52)(47,56)(53,57);(26,29,40,54,31,42,30,41)(27,33,43,53,34,47,35,39)(28,36,49,55,37,50,38,51)(32,44,52,57,46,56,45,48)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2657);