Finite Group DatabasebetaFinite Group Databasebeta| order | 13792 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C2 |
| unambiguous semidirect product | Dic431⋊C8 |
| Sylow | C431 ⋊ C4⋊C8 |
38 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13792 |
Polycyclic presentation:
2^5,431|a^2=d,b^2=c,d^2=e,b^a=bc,f^b=f^4303460 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4⋊C8×D431, C2×Dic431⋊C8, #42119081, … |
| maximal normal subgroup of | C4⋊C8×D431, C2×Dic431⋊C8, #42119081, … |
| maximal quotient of | #42118809, #42118811, #42118813, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13792, 75);