Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Fitting | C2×#104×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2040 |
290 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 69 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|c^2=dg,e^2=g,f^2=g,b^a=bd,c^a=ce,e^a=eg,c^b=cf,f^b=fg,h^b=h^78,e^c=eg,f^c=fg,h^c=h^781118 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2040×D79, C2×#23764628, #34315914, … |
| maximal normal subgroup of | #2040×D79, C2×#23764628, #34315914, … |
| maximal quotient of | #34191597, #34191602, #34191604, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 5738);