Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23×C4 · Schur multiplier (H2) = C25 |
No aliases for this group.
| Fitting | C4×C4⋊C4×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2360 |
620 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=g,b^2=g,d^2=e,b^a=be,c^a=cf,h^a=h^78,d^b=de,h^c=h^781610 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34308521, #34308528, #34308596, … |
| maximal normal subgroup of | #34308521, #34308528, #34308596, … |
| maximal quotient of | C4⋊C4×(C2×D79)⋊C4, #34209779, #34209810, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 7517);