Finite Group DatabasebetaFinite Group Databasebeta| order | 13792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | M16×C431 ⋊ C2 |
| Sylow | C431 ⋊ #137 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 6896 |
Polycyclic presentation:
2^5,431|b^2=e,d^2=e,b^a=bd,c^a=ce,d^a=de,f^a=f^430,d^b=de,f^b=f^4302161 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #42119238, #42119239, #42119243, … |
| maximal normal subgroup of | #42119238, #42119239, #42119243, … |
| maximal quotient of | #42119061, #42119069, #42119101, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13792, 179);