Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #3068 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C27 |
| direct product | C17×#21000 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | C2×#121 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| socle | C2×C17 | C2×#386 |
| prime radical | C2×C17×#575 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
1704 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 544 |
A minimal faithful permutation representation — 4 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24,29,38)(21,31,32,43)(22,27)(23,26)(25,33,40,35)(28,44)(30,39,34,42)(36,41)(37,47)(45,48)(46,49);(18,20)(19,24,26,38)(21,28)(22,34)(23,29)(25,37,40,49)(27,42,41,39)(30,36)(31,48,43,44)(32,45)(33,47)(35,46);(18,21)(19,25)(20,28)(22,35)(23,32)(24,37)(26,40)(27,43)(29,45)(30,47)(31,41)(33,36)(34,46)(38,49)(39,48)(42,44);(20,29)(24,38)(28,45)(30,34)(37,49)(39,42)(44,48)(46,47)986 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 13988);