Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C4×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#60215 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C8×C17 | C24 |
| commutator | C22 | C24×C4×C17 |
| Frattini, cosocle | C2×C4 | C25×C17 |
| socle | C22×C17 | C24×C4 |
| prime radical | C17×#3475 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C8×C17 ◁ G | |
1970 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,23)(21,22)(24,25)(26,27,30,34,31,28,32,36)(29,33,38,40,37,35,39,41);(19,22)(23,25);(26,28,30,36,31,27,32,34)(29,35,38,41,37,33,39,40);(18,20,21,24)(19,23,22,25)(26,29)(27,33)(28,35)(30,38)(31,37)(32,39)(34,40)(36,41);(29,37)(33,35)(38,39)(40,41)1700 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53203);