Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#10752 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator | C2×C4 | C2×C42×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C22×C17 | #379 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C4×C17 ◁ G | |
1222 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)(22,23,27,31,28,32,26,39)(24,33,35,29,36,44,40,43)(25,30,37,46,38,47,41,45)(34,49,52,53,51,48,50,42);(18,19,20,21)(22,24)(23,29)(25,34)(26,40)(27,35)(28,36)(30,42)(31,44)(32,43)(33,39)(37,52)(38,51)(41,50)(45,48)(46,49)(47,53);(22,25)(23,30)(24,34)(26,41)(27,37)(28,38)(29,42)(31,46)(32,47)(33,48)(35,52)(36,51)(39,45)(40,50)(43,53)(44,49)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 3740);