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C3×C7⋊(C19⋊AGL(1,𝔽5)) #22547701

order7980
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7⋊(C19⋊AGL(1,𝔽5))

Splittings

Fitting, socle, HallC3×C5×C7×C19 ⋊ C4
derived, HallC5×C7×C19 ⋊ C3×C4
HallC3×C7×C19 ⋊ AGL(1,𝔽5)
HallC3×C5×C19 ⋊ Dic7
HallC7×C19 ⋊ C3×AGL(1,𝔽5)
HallC3×C5×C7 ⋊ Dic19
HallC5×C19 ⋊ C3×Dic7
HallC3×C19 ⋊ C7⋊AGL(1,𝔽5)
HallC5×C7 ⋊ C3×Dic19
HallC3×C7 ⋊ C19⋊AGL(1,𝔽5)
SylowC19 ⋊ C3×C7⋊AGL(1,𝔽5)
HallC3×C5 ⋊ Dic133
SylowC7 ⋊ C3×C19⋊AGL(1,𝔽5)
SylowC5 ⋊ C3×Dic133

Subgroups

subgroupG/H
center, hypercenterC3C7⋊(C19⋊AGL(1,𝔽5))
commutator, hypocenterC5×C7×C19C3×C4
FrattiniC1G
Fitting, socleC3×C5×C7×C19C4
LCSG ▷ C5×C7×C19
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

807 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#37560925, #37560926, (C7⋊C9)⋊(C19⋊AGL(1,𝔽5)), …
maximal normal subgroup of#37560925, #37560926, (C7⋊C9)⋊(C19⋊AGL(1,𝔽5)), …
maximal quotient ofC9×C7⋊(C19⋊AGL(1,𝔽5)), C32×C7⋊(C19⋊AGL(1,𝔽5)), C3×C3⋊(C7⋊(C19⋊AGL(1,𝔽5)))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 126);