Finite Group DatabasebetaFinite Group Databasebeta| order | 10072 |
| automorphism | Aut(G) order 12670576 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2518 |
| unambiguous semidirect product | C1259⋊Q8 |
| Sylow | C1259 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1259 |
| commutator, socle, prime radical, cosocle | C2×C1259 | C22 |
| Fitting | C4×C1259 | C2 |
| hypercenter | C4 | D1259 |
| hypocenter | C1259 | Q8 |
| LCS | G ▷ C2×C1259 ▷ C1259 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1259|a^2=c,b^2=c,b^a=bc,d^b=d^12582521 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #34117856, #34117857, #34117858, … |
| maximal normal subgroup of | #34117856, #34117857, #34117858, … |
| maximal quotient of | Dic1259⋊C4, C4⋊Dic1259, C2×Dic2518, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10072, 11);