Finite Group DatabasebetaFinite Group Databasebeta| order | 10408 |
| automorphism | Aut(G) order 13530400 |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2602 |
| unambiguous semidirect product | C1301⋊Q8 |
| Sylow | C1301 ⋊ Q8 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C2×D1301 |
| commutator, socle, prime radical, cosocle | C2×C1301 | C22 |
| Fitting | C4×C1301 | C2 |
| hypercenter | C4 | D1301 |
| hypocenter | C1301 | Q8 |
| LCS | G ▷ C2×C1301 ▷ C1301 | |
| UCS | C1 ◁ C2 ◁ C4 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^3,1301|a^2=c,b^2=c,b^a=bc,d^b=d^13002605 conjugacy classes. The character table is too large to display.
| maximal subgroup of | #35209606, #35209607, #35209608, … |
| maximal normal subgroup of | #35209606, #35209607, #35209608, … |
| maximal quotient of | #35209597, C4⋊Dic1301, C2×Dic2602, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10408, 11);