Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of #1619 |
| automorphism | ? |
| homology | Abelianization (H1) = C24×C17 · Schur multiplier (H2) = C26 |
| direct product | C2×C17×#1641 |
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C17 | #120 |
| commutator, Frattini, cosocle | C42 | C24×C17 |
| prime radical | C2×C17×#550 | C2 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C17 ◁ C2×C42×C17 ◁ G | |
1290 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 43 points:
(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(3,4)(5,7)(6,9)(8,10)(11,12,15,18)(13,19,20,26)(14,22,23,17)(16,24,25,21);(4,7)(5,10)(8,9)(14,23)(17,22)(19,26)(21,24);(11,13,15,20)(12,16,18,25)(14,24,23,21)(17,26,22,19)884 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 11499);