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 ⋊ #2452 |
620 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=ef,b^2=f,c^2=f,d^2=e,b^a=be,c^a=cf,d^a=de,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 | #2452×D79, C2×#23767249, #34456187, … |
| maximal normal subgroup of | #2452×D79, C2×#23767249, #34456187, … |
| maximal quotient of | #34210291, #34210639, #34211149, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 8359);