Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | C2×C4⋊Q8×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2491 |
632 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=ef,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^78,c^b=cg,h^b=h^78,h^c=h^781130 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34356303, #34356307, #34356363, … |
| maximal normal subgroup of | #34356303, #34356307, #34356363, … |
| maximal quotient of | #34210223, #34210622, #34211368, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 8876);