Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2593 |
440 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=eg,b^2=eg,c^2=g,d^2=f,b^a=be,c^a=cf,d^a=de,c^b=cg,h^c=h^781598 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2593×D79, C2×#23768891, #34458864, … |
| maximal normal subgroup of | #2593×D79, C2×#23768891, #34458864, … |
| maximal quotient of | #34210698, #34210704, #34211803, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 10001);