Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C23×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2474 |
526 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=ef,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^78,c^b=cg1598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2474×D79, C2×#23767556, #34456664, … |
| maximal normal subgroup of | #2474×D79, C2×#23767556, #34456664, … |
| maximal quotient of | #34210435, #34210831, #34211247, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 8666);