Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1999 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9868 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C17 | C2×D4 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle, prime radical | C23×C17 | C2×C22⋊C4 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C17 ◁ C43×C17 ◁ G | |
512 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 4352 |
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)(18,19)(20,24)(21,22)(23,25)(27,31,32,33)(34,35,37,39,38,41,36,40);(19,22)(23,24)(26,27,29,33,30,32,28,31)(35,39)(36,37)(40,41);(18,20,21,25)(19,23,22,24)(26,28,30,29)(27,31,32,33)(34,36,38,37)(35,40,41,39)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2856);