Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17547 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#17615 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C22×C22⋊C4 |
| commutator | C2×C4 | C23×C4×C17 |
| Frattini, cosocle | C22×C4 | C24×C17 |
| prime radical | C17×#3505 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C4×D4×C17 ◁ G | |
1038 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)(19,24,26,38)(21,33)(25,37,40,48)(27,39,28,34)(30,44)(35,47)(41,49,42,45)(43,46);(18,19)(20,25)(21,34)(22,27)(23,28)(24,35)(26,36)(29,40)(30,45)(31,41)(32,42)(33,38)(37,46)(39,47)(43,49)(44,48);(18,20,22,31)(19,25,27,41)(21,30,33,44)(23,32,36,29)(24,37,39,49)(26,40,28,42)(34,45,38,48)(35,46,47,43);(20,29)(25,40)(30,43)(31,32)(37,48)(41,42)(44,46)(45,49)1037 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10603);