Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #2809 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator, socle, prime radical, cosocle | C23×C79 | C24 |
| Fitting | #398×C79 | C2 |
| hypercenter | #398 | D79 |
| hypocenter | C79 | #2809 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #398 | |
368 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=eg,b^2=ef,c^2=fg,d^2=ef,b^a=be,c^a=cf,d^a=def,c^b=cg,d^b=de,h^b=h^78,h^c=h^78,h^d=h^78890 conjugacy classes — view the full character table.
| maximal subgroup of | #34502791, #34502796, #34502798, … |
| maximal normal subgroup of | #34502791, #34502796, #34502798, … |
| maximal quotient of | #34216740, #34216742, #34216957, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 12497);