Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C26 |
No aliases for this group.
| Fitting | C2×C4×D4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2361 |
788 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=eg,d^2=e,b^a=be,c^a=cf,h^a=h^78,d^b=de,h^d=h^781610 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2361×D79, C2×#23766417, #34447828, … |
| maximal normal subgroup of | #2361×D79, C2×#23766417, #34447828, … |
| maximal quotient of | C22⋊C4×Dic79⋊C4, #34209764, #34209767, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7527);