Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13190 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C8×C17 | C23 |
| commutator | C23 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C23×C17 | C22×C8 |
| prime radical | C22×D4×C17 | C8 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C8×C17 ◁ G | |
522 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,21)(23,25)(26,27,31,35,32,34,39,40,30,28,33,37,29,36,38,41);(18,19,20,21)(26,28,31,37,32,36,39,41,30,27,33,35,29,34,38,40);(22,23,24,25)(26,29,30,32)(27,34,28,36)(31,38,33,39)(35,40,37,41)1496 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6178);