Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #2290 |
696 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,h^b=h^78,h^d=h^781148 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2290×D79, C2×#23765840, #34446670, … |
| maximal normal subgroup of | #2290×D79, C2×#23765840, #34446670, … |
| maximal quotient of | #34209365, #34209396, #34209406, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6950);