Finite Group Databasebeta

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C2×C3×C5×D143 #22575194

order8580
isoclinismisoclinic class of D143
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D143

Splittings

Fitting, socleC2×C3×C5×C11×C13 ⋊ C2
derived, HallC11×C13 ⋊ C22×C3×C5
HallC3×C5×C11×C13 ⋊ C22
HallC5×C11×C13 ⋊ C22×C3
HallC3×C11×C13 ⋊ C22×C5
HallC3×C5×C13 ⋊ C2×D11
HallC3×C5×C11 ⋊ C2×D13
HallC5×C13 ⋊ C2×C3×D11
HallC5×C11 ⋊ C2×C3×D13
HallC3×C13 ⋊ C2×C5×D11
HallC3×C11 ⋊ C2×C5×D13
SylowC13 ⋊ C2×C3×C5×D11
SylowC11 ⋊ C2×C3×C5×D13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D143
commutator, hypocenterC11×C13C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C13C2
LCSG ▷ C11×C13
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2190 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C11⋊(D13⋊C9), C2×C5×C9×D143, C2×C3×C5×C11⋊(D13⋊C3), …
maximal normal subgroup ofC2×C5×C11⋊(D13⋊C9), C2×C5×C9×D143, C2×C3×C5×C11⋊(D13⋊C3), …
maximal quotient ofC2×C5×C9×D143, C3×C5×D3×D143, C2×C32×C5×D143, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 166);