Finite Group DatabasebetaFinite Group Databasebeta| order | 34624 |
| automorphism | ? |
| homology | Abelianization (H1) = C4×C8 · Schur multiplier (H2) = C23 |
| unambiguous semidirect product | (C2×#14524194)⋊C8 |
| Fitting | C2×C8×C541 ⋊ C4 |
| Sylow | C541 ⋊ #336 |
118 conjugacy classes of subgroups.
| transitive degree | μt(G) = 8656 |
Polycyclic presentation:
2^6,541|a^2=d,b^2=e,d^2=f,b^a=bc,g^b=g^52,g^e=g^5402200 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(34624, 1414);