Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61917 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C17×#3207 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1696 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 49 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,28)(21,25)(22,26)(23,27)(24,30)(29,33)(31,32)(34,35,38,42)(36,43,45,48)(37,41,39,46)(40,47,49,44);(18,20,23,30)(19,24,27,28)(21,29,22,31)(25,32,26,33)(34,35)(36,40)(37,46)(38,42)(39,41)(43,44)(45,49)(47,48);(18,21,23,22)(19,25,27,26)(20,29,30,31)(24,32,28,33)(34,36)(35,40)(37,44)(38,45)(39,47)(41,48)(42,49)(43,46);(18,22,23,21)(19,26,27,25)(20,29,30,31)(24,32,28,33)(34,37,38,39)(35,41,42,46)(36,44,45,47)(40,48,49,43);(19,27)(24,28)(25,26)(32,33)(35,42)(40,49)(41,46)(43,48)833 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54905);