Finite Group Databasebeta

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C2×C3×C7×D95 #22547759

order7980
isoclinismisoclinic class of D95
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D95
unambiguous semidirect product(C2×C5)⋊(C3×C7×D19)

Splittings

Fitting, socleC2×C3×C5×C7×C19 ⋊ C2
derived, HallC5×C19 ⋊ C22×C3×C7
HallC3×C5×C7×C19 ⋊ C22
HallC5×C7×C19 ⋊ C22×C3
HallC3×C7×C19 ⋊ C2×D5
HallC3×C5×C19 ⋊ C22×C7
HallC7×C19 ⋊ C2×C3×D5
HallC3×C5×C7 ⋊ C2×D19
HallC3×C19 ⋊ C2×C7×D5
HallC5×C7 ⋊ C2×C3×D19
SylowC19 ⋊ C2×C3×C7×D5
HallC3×C5 ⋊ C2×C7×D19
SylowC5 ⋊ C2×C3×C7×D19

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D95
commutator, hypocenterC5×C19C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C19C2
LCSG ▷ C5×C19
UCSC1 ◁ C2×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2058 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C5⋊(#4294⋊C2), C2×C5⋊#14558780, C2×C5⋊#14558781, …
maximal normal subgroup ofC2×C7×C5⋊(#4294⋊C2), C2×C5⋊#14558780, C2×C5⋊#14558781, …
maximal quotient ofC2×C7×C9×D95, C3×D3×C7×D95, C2×C32×C7×D95, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 184);