Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12948 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C23 |
| direct product | C17×#12949 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1864 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#135 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C17×#405 ◁ G | |
394 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)(18,19,23,30,25,31,24,42)(20,32,34,46,36,43,35,47)(21,37,40,29,22,26,38,28)(27,39,44,33,45,41,48,49);(19,26,31,37)(21,38)(22,40)(23,24)(27,43,45,32)(28,30,29,42)(33,39)(34,35)(41,49)(44,46,48,47);(18,20)(19,27)(21,39)(22,41)(23,35)(24,34)(25,36)(26,43)(28,46)(29,47)(30,48)(31,45)(32,37)(33,38)(40,49)(42,44)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5937);