Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C25 |
| direct product | C17×#19012 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C2×#120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C2×C42×C17 ◁ G | |
844 conjugacy classes of subgroups.
| minimal degree | μ(G) = 49 |
| transitive degree | μt(G) = 2176 |
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)(21,22)(25,32)(26,29)(27,30)(31,33)(34,35)(36,43)(37,41)(38,46)(39,42)(40,44)(45,48)(47,49);(18,19,23,26)(20,25,28,33)(21,24,22,29)(27,31,30,32)(34,35)(36,40)(37,41)(38,46)(39,42)(43,47)(44,48)(45,49);(18,20)(19,25)(21,27)(22,30)(23,28)(24,31)(26,33)(29,32)(34,36)(35,40)(37,44)(38,47)(39,45)(41,48)(42,49)(43,46);(18,21,23,22)(19,24,26,29)(20,27,28,30)(25,31,33,32)(34,37,39,38)(35,41,42,46)(36,44,45,47)(40,48,49,43)578 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 12000);