Finite Group DatabasebetaFinite Group Databasebeta| order | 10804 |
| automorphism | ? |
| homology | Abelianization (H1) = C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting, socle, derived, Hall | C37×C73 ⋊ C4 |
| Sylow | C73 ⋊ #3866 |
| Sylow | C37 ⋊ #64408 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C37×C73 | C4 |
| prime radical, cosocle | D2701 | C2 |
| LCS | G ▷ C37×C73 | |
| UCS | C1 | |
12 conjugacy classes of subgroups.
Polycyclic presentation:
2^2,37,73|a^2=b,c^a=c^31,d^a=d^46,c^b=c^36,d^b=d^72679 conjugacy classes — view the full character table.
| maximal subgroup of | #44569427, #44569428, #44569432, … |
| maximal normal subgroup of | #44569427, #44569428, #44569432, … |
| maximal quotient of | C3×#24925159, C3⋊#24925159 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(10804, 9);