Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C4×C17 · Schur multiplier (H2) = C26 |
| direct product | C17×#11032 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C17 | #392 |
| commutator | C22×C4 | C22×C4×C17 |
| Frattini, cosocle | C23×C4 | C23×C17 |
| socle | C2×C17 | #1438 |
| prime radical | C2×C17×#575 | C2 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C17 ◁ C23×C4×C17 ◁ G | |
1252 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)(18,19,23,27,24,28,22,29)(20,30,32,25,33,42,39,41)(21,34,36,44,38,26,37,45)(31,46,35,40,48,43,47,49);(18,20)(19,25)(21,35)(22,39)(23,32)(24,33)(26,43)(27,42)(28,41)(29,30)(31,37)(34,46)(36,48)(38,47)(40,44)(45,49);(18,21)(19,26)(20,31)(22,36)(23,37)(24,38)(25,40)(27,44)(28,34)(29,45)(30,43)(32,47)(33,48)(35,39)(41,49)(42,46)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4020);