Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C22⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2472 |
786 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|b^2=f,c^2=e,d^2=f,b^a=be,c^a=cf,d^a=de,h^a=h^78,c^b=cg,h^b=h^78,h^c=h^78,h^d=h^781130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2472×D79, C2×#23767533, #34456055, … |
| maximal normal subgroup of | #2472×D79, C2×#23767533, #34456055, … |
| maximal quotient of | #34210190, #34210423, #34211261, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 8643);