Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #2048 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#11186 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #394 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1440 |
| prime radical | C22×#41×C17 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
820 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)(20,30,34,25)(21,35)(22,29)(23,28)(24,27)(26,37)(31,47,48,43)(32,41,33,42)(36,46,49,40)(38,45)(39,44);(18,20)(19,25)(21,36)(22,33)(23,32)(24,34)(26,43)(27,30)(28,42)(29,41)(31,37)(35,40)(38,49)(39,48)(44,47)(45,46);(18,21)(19,26,27,44)(20,31)(22,37)(23,39)(24,38)(25,40,30,46)(28,35,29,45)(32,36)(33,49)(34,48)(41,43,42,47)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4174);