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×#17604 |
| 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×#3494 | C2 |
| LCS | G ▷ C2×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C17×#117 ◁ G | |
1004 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)(19,24,26,37)(21,32)(25,36,40,47)(27,38,28,33)(30,44)(34,46)(39,45,41,48)(42,49);(18,19)(20,25)(21,33)(22,27)(23,28)(24,34)(26,35)(29,39)(30,45)(31,41)(32,37)(36,42)(38,46)(40,43)(44,47)(48,49);(18,20,22,31)(19,25,27,41)(21,30,32,44)(23,29,35,43)(24,36,38,48)(26,40,28,39)(33,45,37,47)(34,42,46,49);(20,29)(25,39)(30,42)(31,43)(36,45)(40,41)(44,49)(47,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 10592);