Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2723 |
498 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=e,b^2=ef,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^c=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34495699, #34495705, #34495799, … |
| maximal normal subgroup of | #34495699, #34495705, #34495799, … |
| maximal quotient of | #34215834, #34215992, #34216007, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 11423);