Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #7694 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C4 |
| direct product | C17×#7713 |
| 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 | |
372 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)(18,19,21,23,22,20,24,25)(26,27,30,32,31,28,29,33)(34,35)(36,42)(37,45)(38,40)(39,43)(41,47)(44,49)(46,48);(18,20)(19,22)(21,23)(24,25)(26,28,31,27)(29,32,30,33)(34,36,38,44)(35,39,40,48)(37,46,47,43)(41,49,45,42);(19,20)(23,25)(26,29,31,30)(27,32,28,33)(35,40)(39,48)(41,45)(42,49)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 701);