Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C28 |
| direct product | C17×#61869 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| prime radical | C2×#41×C17 | C23 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C17×#533 ◁ G | |
1644 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)(20,26)(21,24)(22,25)(23,28)(27,32)(29,31)(30,33)(34,35,39,43)(36,40,45,49)(37,42,38,47)(41,46,48,44);(18,20,22,28)(19,23,25,26)(21,29,30,27)(24,32,33,31)(34,36)(35,40)(37,46)(38,44)(39,45)(41,47)(42,48)(43,49);(34,36)(35,41)(37,44)(38,46)(39,45)(40,47)(42,49)(43,48);(18,21,22,30)(19,24,25,33)(20,27,28,29)(23,31,26,32)(34,37,39,38)(35,42,43,47)(36,44,45,46)(40,41,49,48);(19,25)(23,26)(24,33)(31,32)(34,37,39,38)(35,42,43,47)(36,44,45,46)(40,41,49,48)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 54857);