Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C4×C22⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2335 |
532 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,d^2=ef,b^a=be,c^a=cf,d^a=de,h^a=h^78,c^b=ce,h^c=h^781604 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2335×D79, C2×#23766192, #34447194, … |
| maximal normal subgroup of | #2335×D79, C2×#23766192, #34447194, … |
| maximal quotient of | #34209534, #34209587, #34209606, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7302);