Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C32 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Sylow | C79 ⋊ M128 |
38 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=c,c^2=d,d^2=e,e^2=f,f^2=g,b^a=bg,h^a=h^782576 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34176075, #34176076, #34176079, … |
| maximal normal subgroup of | #34176075, #34176076, #34176079, … |
| maximal quotient of | #34176074, C22⋊(C79⋊C64), C4⋊(C79⋊C64), … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2721);