Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12077 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13039 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | #442 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C22×C4×C17 ◁ C2×C17×#97 ◁ G | |
472 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)(19,21)(22,23,28,34,38,53,26,45,30,36,27,47,29,35,46,33)(24,37,39,51,48,32,44,50,41,52,43,31,40,49,25,42);(18,19,20,21)(22,24,38,40,30,41,29,48)(23,31,35,42,36,51,53,50)(25,26,43,27,44,46,39,28)(32,34,52,33,49,47,37,45);(22,25)(23,32)(24,26)(27,40)(28,48)(29,39)(30,44)(31,34)(33,42)(35,52)(36,49)(37,53)(38,43)(41,46)(45,50)(47,51)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6027);