Finite Group DatabasebetaFinite Group Databasebeta| order | 10804 |
| automorphism | Aut(G) order 14001984 |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
| dicyclic | Dic2701 |
| derived, Hall | C37×C73 ⋊ C4 |
| Sylow | C73 ⋊ Dic37 |
| Sylow | C37 ⋊ Dic73 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D2701 |
| commutator, hypocenter | C37×C73 | C4 |
| Fitting, socle, prime radical, cosocle | C2×C37×C73 | C2 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 ◁ C2 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2,37,73,2|a^2=d,b^a=b^36,c^a=c^722704 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C3×Dic2701, Dic8103, #44569418, … |
| maximal normal subgroup of | C3×Dic2701, #44569418, #44569419, … |
| maximal quotient of | C3×Dic2701, Dic8103, Dic13505 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10804, 4);