Finite Group DatabasebetaFinite Group Databasebeta| order | 10172 |
| automorphism | Aut(G) order 12928612 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2543 |
| unambiguous semidirect product | C2543⋊C4 |
| derived, Sylow | C2543 ⋊ C4 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2543 |
| commutator, hypocenter | C2543 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C2543 | C2 |
| LCS | G ▷ C2543 | |
| UCS | C1 ◁ C2 | |
6 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,2543|a^2=b,c^a=c^25422546 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C4×D2543, C2×Dic2543, C22⋊D2543, … |
| maximal normal subgroup of | C4×D2543, C2×Dic2543, C22⋊D2543, … |
| maximal quotient of | C2543⋊C8, C2×Dic2543, C3×Dic2543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10172, 1);