Finite Group Databasebeta

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C4×C5×#87704 #22547579

order7980
isoclinismisoclinic class of #87704
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC4×C5×#87704

Splittings

Fitting, HallC4×C5×C7×C19 ⋊ C3
derived, HallC7×C19 ⋊ C3×C4×C5
HallC5×C7×C19 ⋊ C3×C4
HallC4×C7×C19 ⋊ C3×C5
HallC4×C5×C19 ⋊ ΓL(1,𝔽8)
HallC4×C5×C7 ⋊ C19⋊C3
HallC5×C19 ⋊ C4×ΓL(1,𝔽8)
HallC4×C19 ⋊ C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C4×C19⋊C3
HallC4×C7 ⋊ C5×C19⋊C3
SylowC19 ⋊ C4×C5×ΓL(1,𝔽8)
SylowC7 ⋊ C4×C5×C19⋊C3

Subgroups

subgroupG/H
center, hypercenterC4×C5#87704
commutator, hypocenterC7×C19C3×C4×C5
FrattiniC2C2×C5×#87704
FittingC4×C5×C7×C19C3
socleC2×C5×C7×C19C2×C3
LCSG ▷ C7×C19
UCSC1 ◁ C4×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

940 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C5×ΓL(1,𝔽8)×C19⋊C3, C5×Dic3×#87704, C3×C4×C5×#87704
maximal normal subgroup ofC4×C5×ΓL(1,𝔽8)×C19⋊C3, C3×C4×C5×#87704
maximal quotient ofC4×C5×#11924776, C5×Dic3×#87704, C3×C4×C5×#87704

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 4);