Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12741 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12743 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1786 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#576 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
926 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)(18,19,22,29,24,28,23,40)(20,30,32,46,33,26,39,45)(21,34,36,47,38,41,37,27)(25,35,43,48,42,49,44,31);(18,20)(19,25)(21,35)(22,32)(23,39)(24,33)(26,41)(27,45)(28,42)(29,43)(30,34)(31,37)(36,48)(38,49)(40,44)(46,47);(18,20)(19,26)(21,31)(22,39)(23,32)(24,33)(25,41)(27,44)(28,30)(29,46)(34,42)(35,37)(36,49)(38,48)(40,45)(43,47)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5731);