Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#11422 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | C2×C22⋊C4 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×C22⋊C8 |
| prime radical | C22×#41×C17 | C4 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C23×C8×C17 ◁ G | |
528 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 1088 |
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)(20,24,25,22)(21,23)(26,27,30,35,31,36,45,53,32,37,46,54,29,34,43,51)(28,38,41,55,40,48,56,52,39,50,44,57,42,33,47,49);(18,20)(19,22)(21,25)(23,24)(26,28)(27,33)(29,42)(30,44)(31,40)(32,39)(34,50)(35,52)(36,38)(37,48)(41,46)(43,56)(45,47)(49,54)(51,55)(53,57);(28,39)(33,48)(38,50)(40,42)(41,44)(47,56)(49,52)(55,57)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4410);