Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C25 · Schur multiplier (H2) = C28 |
No aliases for this group.
| Fitting | C2×C4×Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3523 |
992 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=f,b^2=f,d^2=f,e^2=fg,b^a=bf,c^a=cg,e^a=ef,h^a=h^78,d^b=df1604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34180156, #34180160, #34255484, … |
| maximal normal subgroup of | #34180156, #34180160, #34255484, … |
| maximal quotient of | #34448509, #34449018, #34449135, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 18606);