Finite Group Databasebeta

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C2×C5×D399 #22547753

order7980
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×D399
unambiguous semidirect product(C2×C3)⋊(C5×D133)
unambiguous semidirect product(C2×C7)⋊(C5×D57)
unambiguous semidirect product(C2×C19)⋊(C5×D21)

Splittings

Fitting, socleC2×C3×C5×C7×C19 ⋊ C2
derived, HallC3×C7×C19 ⋊ C22×C5
HallC3×C5×C7×C19 ⋊ C22
HallC5×C7×C19 ⋊ C2×D3
HallC3×C5×C19 ⋊ C2×D7
HallC7×C19 ⋊ C2×C5×D3
HallC3×C5×C7 ⋊ C2×D19
HallC5×C19 ⋊ C2×D21
HallC3×C19 ⋊ C2×C5×D7
HallC5×C7 ⋊ C2×D57
HallC3×C7 ⋊ C2×C5×D19
SylowC19 ⋊ C2×C5×D21
HallC3×C5 ⋊ C2×D133
SylowC7 ⋊ C2×C5×D57
SylowC3 ⋊ C2×C5×D133

Subgroups

subgroupG/H
center, hypercenterC2×C5D399
commutator, hypocenterC3×C7×C19C22×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C19C2
LCSG ▷ C3×C7×C19
UCSC1 ◁ C2×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2010 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×D1197, C2×C5×C3⋊#11716327, C2×C5×C3⋊#11716328, …
maximal normal subgroup ofC2×C5×C3⋊#11716327, C2×C5×C3⋊#11716328, C2×C5×C3⋊(ΓL(1,𝔽8)⋊D19), …
maximal quotient ofC2×C5×D1197, C5×D3×D399, C2×C3×C5×D399, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 178);