Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C42 · Schur multiplier (H2) = C23 |
No aliases for this group.
| Sylow | C79 ⋊ #1390 |
234 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 57 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Polycyclic presentation:
2^7,79|a^2=d,b^2=e,b^a=bc,c^a=cf,f^a=fg,h^a=h^78,d^b=df,h^b=h^78,d^c=dg884 conjugacy classes — view the full character table.
| maximal subgroup of | #1390×D79, C2×#23761519, #34203210, … |
| maximal normal subgroup of | #1390×D79, C2×#23761519, #34203210, … |
| maximal quotient of | #34175227, #34175265, #34175266, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2629);