Finite Group DatabasebetaFinite Group Databasebeta| order | 13792 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Fitting | SD16×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,d^b=de,f^c=f^4301516 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #137×D431, C2×#28352218, #42119855, … |
| maximal normal subgroup of | #137×D431, C2×#28352218, #42119855, … |
| maximal quotient of | #42119057, #42119066, #42119098, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13792, 175);