Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C128 · Schur multiplier (H2) = C1 |
| unambiguous semidirect product | C79⋊C128 |
| derived, Sylow | C79 ⋊ C128 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C64 | D79 |
| commutator, hypocenter | C79 | C128 |
| Fitting, cosocle | C64×C79 | C2 |
| socle, prime radical | C2×C79 | C64 |
| LCS | G ▷ C79 | |
| UCS | C1 ◁ C64 | |
16 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=b,b^2=c,c^2=d,d^2=e,e^2=f,f^2=g,h^a=h^782624 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C128×D79, C2×C79⋊C128, #34176179, … |
| maximal normal subgroup of | C128×D79, C2×C79⋊C128, #34176179, … |
| maximal quotient of | C79⋊C256, C2×C79⋊C128 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 2329);