Finite Group Databasebeta

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C2×C3×D455 #19129886

order5460
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D455
unambiguous semidirect product(C2×C5)⋊(C3×D91)

Splittings

Fitting, socleC2×C3×C5×C7×C13 ⋊ C2
derived, HallC5×C7×C13 ⋊ C22×C3
HallC3×C5×C7×C13 ⋊ C22
HallC3×C7×C13 ⋊ C2×D5
HallC3×C5×C13 ⋊ C2×D7
HallC3×C5×C7 ⋊ C2×D13
HallC7×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×C3×D7
HallC3×C13 ⋊ C2×D35
HallC5×C7 ⋊ C2×C3×D13
HallC3×C7 ⋊ C2×D65
HallC3×C5 ⋊ C2×D91
SylowC13 ⋊ C2×C3×D35
SylowC7 ⋊ C2×C3×D65
SylowC5 ⋊ C2×C3×D91

Subgroups

subgroupG/H
center, hypercenterC2×C3D455
commutator, hypocenterC5×C7×C13C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C7×C13C2
LCSG ▷ C5×C7×C13
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1374 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊#13109902, C2×C5⋊#13109903, C2×C5⋊((C7⋊C9)⋊D13), …
maximal normal subgroup ofC2×C5⋊#13109902, C2×C5⋊#13109903, C2×C5⋊((C7⋊C9)⋊D13), …
maximal quotient ofC2×C9×D455, C3×D3×D455, C2×C3×D1365, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 228);