Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #12750 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#12750 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1786 |
| commutator | C2×C8 | C22×C4×C17 |
| Frattini, cosocle | C22×C8 | C23×C17 |
| prime radical | C2×C17×#576 | C2 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C22×C4×C17 ◁ C2×C17×#131 ◁ G | |
928 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)(20,30,33,45)(21,35)(22,27)(23,29)(24,31,41,48)(25,32,42,34)(26,37)(28,39)(36,46,49,40)(38,43)(44,47);(18,20)(19,24)(21,36)(22,32)(23,33)(25,26)(27,40)(28,46)(29,41)(30,43)(31,47)(34,39)(35,45)(37,48)(38,49)(42,44);(18,20)(19,25)(21,31)(22,34)(23,33)(24,26)(27,45)(28,30)(29,42)(32,39)(35,40)(36,47)(37,49)(38,48)(41,44)(43,46)680 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 5738);