Finite Group DatabasebetaFinite Group Databasebeta| order | 760 |
| automorphism | ? |
| homology | Abelianization (H1) = C22 · Schur multiplier (H2) = C2 |
No aliases for this group.
| Hall | C5×C19 ⋊ D4 |
| Sylow | C19 ⋊ D20 |
| Sylow | C5 ⋊ C22⋊D19 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C2 | D5×D19 |
| commutator, Fitting, socle, cosocle | C2×C5×C19 | C22 |
| hypocenter | C5×C19 | D4 |
| LCS | G ▷ C2×C5×C19 ▷ C5×C19 | |
| UCS | C1 ◁ C2 | |
32 conjugacy classes of subgroups.
| minimal degree | μ(G) = 28 |
| transitive degree | μt(G) = 380 |
Polycyclic presentation:
2^3,5,19|a^2=c,b^a=bc,e^a=e^18,d^b=d^485 conjugacy classes — view the full character table.
| maximal subgroup of | #13095129, #13095130, #13095132, … |
| maximal normal subgroup of | #13095129, #13095130, #13095132, … |
| maximal quotient of | #13095031, #13095036, #13095037, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(760, 12);