Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2674 |
562 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=e,b^2=e,c^2=e,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^781124 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34495043, #34495046, #34495114, … |
| maximal normal subgroup of | #34495043, #34495046, #34495114, … |
| maximal quotient of | #34215586, #34215650, #34215904, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 10787);