Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#9056 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C17 | #120 |
| commutator | C42 | C22×C4×C17 |
| Frattini, cosocle | C2×C42 | C23×C17 |
| socle | C22×C17 | #386 |
| prime radical | C23×C17 | #121 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C17 ◁ C2×C42×C17 ◁ G | |
432 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 1088 |
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)(19,23,25,28)(20,26,27,29)(34,35)(36,44,47,48)(37,41,40,46)(38,42)(39,43)(45,49);(18,19,21,28,22,25,30,23)(20,24,29,32,27,33,26,31)(34,36,45,46,39,47,38,41)(35,40,49,44,43,37,42,48);(18,20)(19,24)(21,29)(22,27)(23,31)(25,33)(26,30)(28,32)(34,37,39,40)(35,41,43,46)(36,42,47,49)(38,44,45,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 2044);