Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C16×C17 · Schur multiplier (H2) = C26 |
| direct product | C2×D4×C16×C17 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C16×C17 | C22 |
| commutator | C2 | C23×C16×C17 |
| Frattini, cosocle | C2×C8 | C24×C17 |
| socle | C23×C17 | C22×C8 |
| prime radical | C22×D4×C17 | C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C16×C17 ◁ G | |
806 conjugacy classes of subgroups.
| minimal degree | μ(G) = 39 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 4 generators on 39 points:
(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39);(3,4,5,6);(4,6);(7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22)2720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 26417);