Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of D4 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C4×C16×C17 · Schur multiplier (H2) = C2×C4 |
| direct product | C16×M16×C17 |
| subgroup | G/H | |
|---|---|---|
| center | C4×C16×C17 | C22 |
| commutator | C2 | C2×C4×C16×C17 |
| Frattini, cosocle | C4×C8 | C23×C17 |
| socle | C22×C17 | C2×C4×C8 |
| prime radical | C23×C17 | C4×C8 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C16×C17 ◁ G | |
306 conjugacy classes of subgroups.
| minimal degree | μ(G) = 41 |
| transitive degree | μt(G) = 2176 |
A minimal faithful permutation representation — 3 generators on 41 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16)(25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41);(17,18,19,20,21,22,23,24);(18,22)(20,24)2720 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 4395);