Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #471 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8×C17 · Schur multiplier (H2) = C22 |
| direct product | C17×#13164 |
| subgroup | G/H | |
|---|---|---|
| center | C8×C17 | #121 |
| commutator | C2×C4 | C22×C8×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1939 |
| prime radical | C23×C17 | #131 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C8×C17 ◁ C22×C8×C17 ◁ G | |
284 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 3 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19,23,29,24,28,39,46,25,30,38,27,22,40,21,37)(20,31,35,48,33,26,41,44,36,43,49,47,34,45,32,42);(18,20,23,35,24,33,39,41,25,36,38,49,22,34,21,32)(19,26,29,44,28,43,46,47,30,45,27,42,40,31,37,48);(18,21,22,38,25,39,24,23)(19,27,28,37,30,29,40,46)(20,32,34,49,36,41,33,35)(26,42,43,48,45,44,31,47)1088 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6152);