Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C22×C4 |
| direct product | C17×#12602 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C22⋊C4 |
| commutator | C22 | C2×C4×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×C22⋊C8 |
| prime radical | C24×C17 | C2×C8 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ C2×C4×C8×C17 ◁ G | |
490 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)(18,19,21,20)(22,23)(24,32)(25,36)(26,31)(27,29)(28,33)(30,38)(34,40)(35,45)(37,49)(39,42)(41,47)(43,50)(44,46)(48,51)(52,53);(22,24,25,34,26,35,37,48,27,33,38,46,39,47,50,53)(23,28,30,40,31,41,43,51,29,32,36,44,42,45,49,52);(18,20,21,19)(23,29)(28,32)(30,36)(31,42)(40,44)(41,45)(43,49)(51,52)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5590);