Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #2563 |
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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=efg,b^2=eg,d^2=e,b^a=be,c^a=cf,d^a=de,h^a=h^78,c^b=cg1598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34185622, #34185624, #34185662, … |
| maximal normal subgroup of | #34185622, #34185624, #34185662, … |
| maximal quotient of | #34210514, #34210549, #34211107, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 9683);