Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #2812 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C17 · Schur multiplier (H2) = C27×C4 |
| direct product | C2×C17×#2821 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C25×C17 | C23 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
2370 conjugacy classes of subgroups.
| minimal degree | μ(G) = 47 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 47 points:
(1,2)(31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47);(7,8,10,12)(9,11,13,14)(16,20)(21,23)(22,26)(29,30);(4,6)(9,13)(11,14)(15,16)(17,23)(18,26)(19,20)(21,25)(22,28)(24,29)(27,30);(3,4)(5,6)(7,8)(9,11)(10,12)(13,14)(15,17,19,25)(16,21,20,23)(18,27,28,24)(22,30,26,29);(7,9)(8,11)(10,13)(12,14)(15,18,19,28)(16,22,20,26)(17,24,25,27)(21,29,23,30)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29674);