Finite Group DatabasebetaFinite Group Databasebeta| order | 10112 |
| automorphism | ? |
| homology | Abelianization (H1) = C24 · Schur multiplier (H2) = C24×C4 |
No aliases for this group.
| Fitting | #393×C79 ⋊ C2 |
| Sylow | C79 ⋊ #2676 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D79 |
| commutator, socle, cosocle | C23×C79 | C24 |
| Fitting | #393×C79 | C2 |
| hypercenter | #393 | D79 |
| hypocenter | C79 | #2676 |
| LCS | G ▷ C23×C79 ▷ C79 | |
| UCS | C1 ◁ C23 ◁ #393 | |
676 conjugacy classes of subgroups.
Polycyclic presentation:
2^7,79|a^2=e,d^2=e,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 | #34495053, #34495065, #34495069, … |
| maximal normal subgroup of | #34495053, #34495065, #34495069, … |
| maximal quotient of | #34215604, #34215622, #34215838, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10112, 10810);