Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #17603 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4×C17 · Schur multiplier (H2) = C24×C4 |
| direct product | C17×#17609 |
| 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×#525 | C22 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
944 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)(21,32)(25,37,41,48)(27,39,28,33)(30,45)(34,36)(40,46,42,49)(43,47);(18,19,22,27)(20,25,31,42)(21,33,32,38)(23,28,35,26)(24,36,39,34)(29,40,44,41)(30,46,45,48)(37,47,49,43);(18,20,22,31)(19,25,27,42)(21,30,32,45)(23,29,35,44)(24,37,39,49)(26,41,28,40)(33,46,38,48)(34,43,36,47);(20,29)(25,40)(30,43)(31,44)(37,46)(41,42)(45,47)(48,49)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10597);