Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 4 |
| isoclinism | isoclinic class of #13096 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C24 |
| direct product | C17×#13102 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C17 | #1898 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C2×#41 | C23×C17 |
| prime radical | C17×#3008 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C17 ◁ C2×C4×C17 ◁ C2×C17×H(5,𝔽2) ◁ G | |
688 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)(18,19,23,26,24,29,22,28)(20,30,34,46,35,48,33,47)(21,36,39,41,38,27,31,44)(25,40,42,37,43,49,45,32);(18,20,31,49)(19,25,41,47)(21,37,22,34)(23,33,38,32)(24,35,39,40)(26,42,36,48)(27,30,28,45)(29,43,44,46);(19,26)(21,38)(22,23)(25,42)(27,44)(28,29)(30,46)(32,37)(33,34)(36,41)(43,45)(47,48)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 6090);