Finite Group Databasebeta

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C2×C3×C7×D5×C19 #22547760

order7980
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C3×C7×C19 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D5×C19
unambiguous semidirect productC5⋊(C22×C3×C7×C19)
unambiguous semidirect product(C2×C5)⋊(C2×C3×C7×C19)

Splittings

Fitting, socleC2×C3×C5×C7×C19 ⋊ C2
derived, SylowC5 ⋊ C22×C3×C7×C19
HallC3×C5×C7×C19 ⋊ C22
HallC5×C7×C19 ⋊ C22×C3
HallC3×C5×C19 ⋊ C22×C7
HallC3×C5×C7 ⋊ C22×C19
HallC5×C19 ⋊ C22×C3×C7
HallC5×C7 ⋊ C22×C3×C19
HallC3×C5 ⋊ C22×C7×C19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7×C19D5
commutator, hypocenterC5C22×C3×C7×C19
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C19C2
LCSG ▷ C5
UCSC1 ◁ C2×C3×C7×C19

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3192 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×D5×#4294, C2×D5×C19×C7⋊C9, C2×D5×#11924776, …
maximal normal subgroup ofC2×C7×D5×#4294, C2×D5×C19×C7⋊C9, C2×D5×#11924776, …
maximal quotient ofC2×C7×C9×D5×C19, C3×D3×C7×D5×C19, C2×C32×C7×D5×C19, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 185);