Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7654 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#7673 |
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C23×C17 | C2×C22⋊C4 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C43×C17 ◁ G | |
384 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 4352 |
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)(19,22)(20,24)(23,25)(27,31,32,33)(34,35,37,41,38,40,46,48)(36,42,44,49,43,39,45,47);(18,19,21,23)(20,25,24,22)(26,27)(28,31)(29,33)(30,32)(34,36,38,43)(35,39,40,42)(37,45,46,44)(41,49,48,47);(26,28,30,29)(27,31,32,33)(36,43)(39,42)(44,45)(47,49)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 661);