Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12933 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12933 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1853 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×#41×C17 | D4 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
380 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)(19,25,28,39)(20,29)(21,32)(22,23)(26,40,42,47)(27,44,37,33)(30,46)(31,36)(34,35)(38,43,49,41);(18,19,23,37,24,28,22,27)(20,26,29,41,31,42,36,43)(21,33,32,25,35,44,34,39)(30,47,45,38,46,40,48,49);(18,20)(19,26)(21,30)(22,36)(23,29)(24,31)(25,38)(27,43)(28,42)(32,45)(33,47)(34,48)(35,46)(37,41)(39,49)(40,44)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5921);