Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C8 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Sylow | C79 ⋊ #2183 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C8 | C22×D79 |
| commutator, socle, prime radical | C22×C79 | C22×C8 |
| Fitting | #346×C79 | C2 |
| cosocle | C2×C8×C79 | C23 |
| hypercenter | #346 | D79 |
| hypocenter | C79 | #2183 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C2×C8 ◁ #346 | |
126 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 71 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=e,b^2=d,c^2=de,e^2=f,f^2=g,b^a=bd,c^a=cg,h^b=h^781616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #2183×D79, C2×#23765306, #34441760, … |
| maximal normal subgroup of | #2183×D79, C2×#23765306, #34441760, … |
| maximal quotient of | #34203617, #34203621, #34203625, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6416);