Finite Group Databasebeta

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C2×C7×D285 #22547751

order7980
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×D285
unambiguous semidirect product(C2×C3)⋊(C7×D95)
unambiguous semidirect product(C2×C5)⋊(C7×D57)
unambiguous semidirect product(C2×C19)⋊(C7×D15)

Splittings

Fitting, socleC2×C3×C5×C7×C19 ⋊ C2
derived, HallC3×C5×C19 ⋊ C22×C7
HallC3×C5×C7×C19 ⋊ C22
HallC5×C7×C19 ⋊ C2×D3
HallC3×C7×C19 ⋊ C2×D5
HallC7×C19 ⋊ C2×D15
HallC3×C5×C7 ⋊ C2×D19
HallC5×C19 ⋊ C2×D3×C7
HallC3×C19 ⋊ C2×C7×D5
HallC5×C7 ⋊ C2×D57
HallC3×C7 ⋊ C2×D95
SylowC19 ⋊ C2×C7×D15
HallC3×C5 ⋊ C2×C7×D19
SylowC5 ⋊ C2×C7×D57
SylowC3 ⋊ C2×C7×D95

Subgroups

subgroupG/H
center, hypercenterC2×C7D285
commutator, hypocenterC3×C5×C19C22×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C19C2
LCSG ▷ C3×C5×C19
UCSC1 ◁ C2×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2016 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×D855, C2×C7×C3⋊(C5⋊(D19⋊C3)), C2×C3⋊(C5⋊#11716321), …
maximal normal subgroup ofC2×C7×C3⋊(C5⋊(D19⋊C3)), C2×C3⋊(C5⋊#11716321), C2×C3⋊(C5⋊#11716322), …
maximal quotient ofC2×C7×D855, D3×C7×D285, C2×C3×C7×D285, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 176);