Finite Group DatabasebetaFinite Group Databasebeta| order | 10232 |
| automorphism | Aut(G) order 13076496 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2558 |
| unambiguous semidirect product | C1279⋊Q8 |
| Sylow | C1279 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1279 |
| commutator, socle, prime radical, cosocle | C2×C1279 | C22 |
| Fitting | C4×C1279 | C2 |
| hypercenter | C4 | D1279 |
| hypocenter | C1279 | Q8 |
| LCS | G ▷ C2×C1279 ▷ C1279 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1279|a^2=c,b^2=c,b^a=bc,d^b=d^12782561 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35205925, #35205926, #35205927, … |
| maximal normal subgroup of | #35205925, #35205926, #35205927, … |
| maximal quotient of | Dic1279⋊C4, C4⋊Dic1279, C2×Dic2558, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10232, 11);