Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C2×#126×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2560 |
518 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=e,b^2=fg,d^2=ef,b^a=be,c^a=cf,d^a=de,c^b=cg,h^b=h^78,h^c=h^781130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2560×D79, C2×#23768542, #34458448, … |
| maximal normal subgroup of | #2560×D79, C2×#23768542, #34458448, … |
| maximal quotient of | #34210631, #34210902, #34211586, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 9652);