Finite Group DatabasebetaFinite Group Databasebeta| order | 4352 |
| nilpotency class | 3 |
| isoclinism | isoclinic class of D8 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C17×C32 · Schur multiplier (H2) = C2 |
| direct product | C17×#7458 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C16×C17 | D4 |
| commutator | C4 | C2×C17×C32 |
| Frattini, cosocle | C4×C16 | C22×C17 |
| socle, prime radical | C22×C17 | C4⋊C16 |
| LCS | G ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C16×C17 ◁ C4×C16×C17 ◁ G | |
98 conjugacy classes of subgroups.
| minimal degree | μ(G) = 57 |
| transitive degree | μt(G) = 4352 |
A minimal faithful permutation representation — 2 generators on 57 points:
(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17)(19,22)(20,23)(24,25)(26,27,28,32,29,33,36,42,30,34,37,43,39,45,48,52,31,35,38,44,40,46,49,53,41,47,50,54,51,55,56,57);(18,19,23,25,21,24,20,22)1904 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(4352, 446);