Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12926 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
400 conjugacy classes of subgroups.
| minimal degree | μ(G) = 53 |
| transitive degree | μt(G) = 2176 |
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)(18,19,21,20)(22,23,28,34)(24,36,25,39)(26,42,45,51)(27,35,29,33)(30,40,49,37)(31,38,50,41)(32,44,47,46)(43,52,53,48);(18,20,21,19)(22,24,28,25)(23,30,34,49)(26,43,45,53)(27,38,29,41)(31,47,50,32)(33,48,35,52)(36,51,39,42)(37,44,40,46);(22,25,28,24)(23,31,34,50)(26,40,45,37)(27,38,29,41)(30,47,49,32)(33,36,35,39)(42,48,51,52)(43,46,53,44)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5914);