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 | C8×Q8×C79 | C2 |
| cosocle | C2×C8×C79 | C23 |
| hypercenter | C8×Q8 | D79 |
| hypocenter | C79 | #2183 |
| LCS | G ▷ C22×C79 ▷ C79 | |
| UCS | C1 ◁ C2×C8 ◁ C8×Q8 | |
126 conjugacy classes of subgroups.
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^a=h^78,h^c=h^781616 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34200039, #34200043, #34200053, … |
| maximal normal subgroup of | #34200039, #34200043, #34200053, … |
| maximal quotient of | #34203618, #34203624, #34205886, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 6419);