Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2457 |
596 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^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 | #2457×D79, C2×#23767307, #34456450, … |
| maximal normal subgroup of | #2457×D79, C2×#23767307, #34456450, … |
| maximal quotient of | #34210325, #34210556, #34211226, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 8417);