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 |
| direct product | C2×C17×#2837 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C17 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C17 |
| prime radical | C23×D4×C17 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C17 ◁ G | |
2110 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 5 generators on 43 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(4,7)(8,10)(11,12)(13,16)(14,15)(17,18)(19,20,23,22)(21,24,25,26);(5,9)(8,10)(12,15)(13,17)(20,22)(24,26);(3,4,6,7)(5,8,9,10)(11,12)(13,18)(14,15)(16,17)(19,21)(20,24)(22,26)(23,25);(3,5)(4,8)(6,9)(7,10)(11,13,14,17)(12,16,15,18)(19,22,23,20)(21,24,25,26)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 29646);