Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C22×C4 |
No aliases for this group.
| Sylow | C79 ⋊ #2769 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator, socle, prime radical, cosocle | C23×C79 | C24 |
| Fitting | #400×C79 | C2 |
| hypercenter | #400 | D79 |
| hypocenter | C79 | #2769 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #400 | |
344 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 121 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=g,b^2=f,c^2=ef,d^2=e,b^a=be,c^a=cf,d^a=def,h^a=h^78,c^b=cg,d^b=de,h^b=h^78,h^d=h^78890 conjugacy classes — view the full character table.
| maximal subgroup of | #34200641, #34200645, #34201227, … |
| maximal normal subgroup of | #34200641, #34200645, #34201227, … |
| maximal quotient of | #34215988, #34216094, #34216102, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 12005);