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C2×C5×D357 #20297488

order7140
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D357
unambiguous semidirect product(C2×C3)⋊(C5×D119)
unambiguous semidirect product(C2×C7)⋊(C5×D51)
unambiguous semidirect product(C2×C17)⋊(C5×D21)

Splittings

Fitting, socleC2×C3×C5×C7×C17 ⋊ C2
derived, HallC3×C7×C17 ⋊ C22×C5
HallC3×C5×C7×C17 ⋊ C22
HallC5×C7×C17 ⋊ C2×D3
HallC3×C5×C17 ⋊ C2×D7
HallC7×C17 ⋊ C2×C5×D3
HallC3×C5×C7 ⋊ C2×D17
HallC5×C17 ⋊ C2×D21
HallC3×C17 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×D51
HallC3×C7 ⋊ C2×C5×D17
SylowC17 ⋊ C2×C5×D21
HallC3×C5 ⋊ C2×D119
SylowC7 ⋊ C2×C5×D51
SylowC3 ⋊ C2×C5×D119

Subgroups

subgroupG/H
center, hypercenterC2×C5D357
commutator, hypocenterC3×C7×C17C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C17C2
LCSG ▷ C3×C7×C17
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1800 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×D1071, C2×C5×C3⋊(C17⋊AGL(1,𝔽7)), C5×D3×D357, …
maximal normal subgroup ofC2×C5×C3⋊(C17⋊AGL(1,𝔽7)), C2×C3×C5×D357, C2×C25×D357, …
maximal quotient ofC2×C5×D1071, C5×D3×D357, C2×C3×C5×D357, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7140, 118);