Finite Group Databasebeta

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C2×C3×D715 #22575190

order8580
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×D715
unambiguous semidirect product(C2×C5)⋊(C3×D143)
unambiguous semidirect product(C2×C11)⋊(C3×D65)

Splittings

Fitting, socleC2×C3×C5×C11×C13 ⋊ C2
derived, HallC5×C11×C13 ⋊ C22×C3
HallC3×C5×C11×C13 ⋊ C22
HallC3×C11×C13 ⋊ C2×D5
HallC3×C5×C13 ⋊ C2×D11
HallC3×C5×C11 ⋊ C2×D13
HallC11×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×C3×D11
HallC5×C11 ⋊ C2×C3×D13
HallC3×C13 ⋊ C2×D55
HallC3×C11 ⋊ C2×D65
HallC3×C5 ⋊ C2×D143
SylowC13 ⋊ C2×C3×D55
SylowC11 ⋊ C2×C3×D65
SylowC5 ⋊ C2×C3×D143

Subgroups

subgroupG/H
center, hypercenterC2×C3D715
commutator, hypocenterC5×C11×C13C22×C3
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C5×C11×C13
UCSC1 ◁ C2×C3

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2154 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5⋊(C11⋊(D13⋊C9)), C2×C9×D715, C2×C3×C5⋊(C11⋊(D13⋊C3)), …
maximal normal subgroup ofC2×C5⋊(C11⋊(D13⋊C9)), C2×C9×D715, C2×C3×C5⋊(C11⋊(D13⋊C3)), …
maximal quotient ofC2×C9×D715, C3×D3×D715, C2×C32×D715, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 162);