Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#10764 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C22⋊C4 |
| commutator | C23 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | C4×C22⋊C4 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C8×C17 ◁ G | |
1194 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)(18,19)(20,21)(22,23)(24,32,34,28)(25,36,37,29)(26,31)(27,30)(33,40)(35,45,48,41)(38,49,50,42)(39,43)(44,47)(46,51)(52,53);(19,21)(22,24,26,35,27,34,39,48)(23,28,31,41,30,32,43,45)(25,33,38,46,37,47,50,53)(29,40,42,51,36,44,49,52);(22,25)(23,29)(24,33)(26,38)(27,37)(28,40)(30,36)(31,42)(32,44)(34,47)(35,46)(39,50)(41,51)(43,49)(45,52)(48,53)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3752);