Finite Group DatabasebetaFinite Group Databasebeta| order | 10552 |
| automorphism | Aut(G) order 13907536 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2638 |
| unambiguous semidirect product | C1319⋊Q8 |
| Sylow | C1319 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1319 |
| commutator, socle, prime radical, cosocle | C2×C1319 | C22 |
| Fitting | C4×C1319 | C2 |
| hypercenter | C4 | D1319 |
| hypocenter | C1319 | Q8 |
| LCS | G ▷ C2×C1319 ▷ C1319 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1319|a^2=c,b^2=c,b^a=bc,d^b=d^13182641 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35231532, #35231533, #35231534, … |
| maximal normal subgroup of | #35231532, #35231533, #35231534, … |
| maximal quotient of | Dic1319⋊C4, C4⋊Dic1319, C2×Dic2638, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10552, 11);