Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C27 |
No aliases for this group.
| Fitting | #386×C79 ⋊ C2 |
| Sylow | C79 ⋊ D4×C22⋊C4 |
1252 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^a=be,c^a=cf,d^b=de,h^c=h^78,h^d=h^781142 conjugacy classes. The character table is too large to display.
| maximal subgroup of | D4×C22⋊C4×D79, C2×#23766218, #34447469, … |
| maximal normal subgroup of | D4×C22⋊C4×D79, C2×#23766218, #34447469, … |
| maximal quotient of | #34209668, #34209670, #34209683, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7328);