Finite Group Databasebeta

← Prev (#22547747) Next (#22547749) →

C22×C5×C7×C19⋊C3 #22547748

order7980
isoclinismisoclinic class of C19⋊C3
automorphism?
homologyAbelianization (H1) = C22×C3×C5×C7 · Schur multiplier (H2) = C2

Aliases

direct productC22×C5×C7×C19⋊C3

Splittings

Fitting, socle, HallC22×C5×C7×C19 ⋊ C3
derived, SylowC19 ⋊ C22×C3×C5×C7
HallC5×C7×C19 ⋊ C22×C3
HallC22×C7×C19 ⋊ C3×C5
HallC22×C5×C19 ⋊ C3×C7
HallC7×C19 ⋊ C22×C3×C5
HallC5×C19 ⋊ C22×C3×C7
HallC22×C19 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC22×C5×C7C19⋊C3
commutator, hypocenterC19C22×C3×C5×C7
FrattiniC1G
Fitting, socleC22×C5×C7×C19C3
LCSG ▷ C19
UCSC1 ◁ C22×C5×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1260 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C7×C22⋊#4296, C5×C7×A4×C19⋊C3, C5×C22⋊#11924780, …
maximal normal subgroup ofC5×C7×C22⋊#4296, C5×C7×A4×C19⋊C3, C5×C22⋊#11924780, …
maximal quotient ofC22×C5×C7×#4294, C2×C5×D3×C7×C19⋊C3, C22×C3×C5×C7×C19⋊C3

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 173);