Finite Group DatabasebetaFinite Group Databasebeta| order | 10212 |
| automorphism | Aut(G) order 8087904 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2553 |
| unambiguous semidirect product | C3⋊Dic851 |
| unambiguous semidirect product | C23⋊Dic111 |
| derived, Hall | C3×C23×C37 ⋊ C4 |
| Hall | C23×C37 ⋊ Dic3 |
| Hall | C3×C37 ⋊ Dic23 |
| Hall | C3×C23 ⋊ Dic37 |
| Sylow | C37 ⋊ Dic69 |
| Sylow | C23 ⋊ Dic111 |
| Sylow | C3 ⋊ Dic851 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2553 |
| commutator, hypocenter | C3×C23×C37 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C3×C23×C37 | C2 |
| LCS | G ▷ C3×C23×C37 | |
| UCS | C1 ◁ C2 | |
24 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,23,37,2|a^2=e,b^a=b^2,c^a=c^22,d^a=d^362556 conjugacy classes. The character table is too large to display.
| maximal subgroup of | Dic7659, C3⋊(C23⋊(Dic37⋊C3)), C3⋊Dic2553, … |
| maximal normal subgroup of | C3⋊(C23⋊(Dic37⋊C3)), C3×Dic2553, Dic5106 |
| maximal quotient of | Dic7659, C3⋊Dic2553, C3×Dic2553, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10212, 9);