Finite Group DatabasebetaFinite Group Databasebeta| order | 7980 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
No aliases for this group.
| subgroup | G/H | |
|---|---|---|
| center, Frattini, hypercenter | C1 | G |
| commutator, Fitting, socle, hypocenter | C5×C7×C19 | C3×C4 |
| LCS | G ▷ C5×C7×C19 | |
| UCS | C1 | |
48 conjugacy classes of subgroups.
Polycyclic presentation:
2,3,2,5,7,19|a^2=c,d^a=d^2,e^a=e^6,e^b=e^2,f^b=f^7,d^c=d^4121 conjugacy classes — view the full character table.
| maximal subgroup of | C19⋊C3×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×#22547634, C3⋊#22547634 |
| maximal normal subgroup of | C19⋊C3×ΓL(1,𝔽8)⋊AGL(1,𝔽5), C3×#22547634 |
| maximal quotient of | #37560927, C3×#22547634, C3⋊#22547634 |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(7980, 59);