Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12944 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #447 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| socle | C2×C17 | #1862 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C22×C4×C17 ◁ C2×C17×#97 ◁ G | |
388 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)(18,19,23,29,25,30,24,43)(20,31,35,47,36,27,40,46)(21,37,34,45,38,44,33,26)(22,39,32,48,42,49,41,28);(18,20,23,35,25,36,24,40)(19,26,29,37,30,45,43,44)(21,32,34,42,38,41,33,22)(27,28,46,39,31,48,47,49);(18,21)(19,27)(20,32)(22,40)(23,34)(24,33)(25,38)(26,28)(29,46)(30,31)(35,42)(36,41)(37,39)(43,47)(44,49)(45,48)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5932);