Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of H(3,ℤ/4) |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#12547 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C42 |
| commutator | C4 | C2×C4×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C22×C17 | C2×#97 |
| prime radical | C24×C17 | M16 |
| LCS | G ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ G | |
586 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)(22,23,26,31,27,33,41,50,28,32,42,49,25,30,39,47)(24,34,37,51,38,29,43,45,35,46,40,53,36,44,52,48);(19,21)(22,24)(23,29,32,44)(25,36)(26,40)(27,38)(28,35)(30,34,33,46)(31,48,49,45)(37,42)(39,43)(41,52)(47,53,50,51);(24,35)(29,44)(34,46)(36,38)(37,40)(43,52)(45,48)(51,53)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5535);