Finite Group DatabasebetaFinite Group Databasebeta| order | 19232 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | C4⋊#18012467 |
| Sylow | C601 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 19232 |
Polycyclic presentation:
2^5,601|a^2=d,b^2=c,d^2=e,b^a=bc,f^a=f^6004820 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4⋊#18012467, #50308405, Q8⋊#18012467, … |
| maximal normal subgroup of | D4⋊#18012467, #50308405, Q8⋊#18012467, … |
| maximal quotient of | #50308427, #50308429, #50308431, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(19232, 76);