Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24 |
No aliases for this group.
| Fitting | C8×D4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #3300 |
386 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=e,b^2=g,c^2=g,f^2=g,b^a=be,c^a=cf,f^a=fg,h^a=h^78,d^b=de,f^c=fg,h^c=h^781595 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #3300×D79, C2×#23775289, #35164750, … |
| maximal normal subgroup of | #3300×D79, C2×#23775289, #35164750, … |
| maximal quotient of | #34303714, #34304496, #34305424, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 16399);