Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #60771 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C17×#60825 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C17 | C23×D4 |
| commutator, Frattini, cosocle | C2×C4 | C25×C17 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C17 ◁ C4×#41×C17 ◁ G | |
2146 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 1088 |
A minimal faithful permutation representation — 5 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(18,19)(20,24)(21,23)(22,25)(27,31)(29,36)(32,37)(33,38)(35,40)(39,41);(18,20,21,25)(19,22,23,24)(27,32)(31,37)(33,39)(38,41);(20,25)(22,24)(26,27)(28,33)(29,37)(30,32)(31,36)(34,39)(35,41)(38,40);(19,23)(22,24)(26,28)(27,33)(29,35)(30,34)(31,38)(32,39)(36,40)(37,41);(28,34)(33,39)(35,40)(38,41)782 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 53813);