Finite Group Databasebeta

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C2×C3×C5×D187 #26014442

order11220
isoclinismisoclinic class of D187
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C5×D187
unambiguous semidirect product(C2×C17)⋊(C3×C5×D11)

Splittings

Fitting, socleC2×C3×C5×C11×C17 ⋊ C2
derived, HallC11×C17 ⋊ C22×C3×C5
HallC3×C5×C11×C17 ⋊ C22
HallC5×C11×C17 ⋊ C22×C3
HallC3×C11×C17 ⋊ C22×C5
HallC3×C5×C17 ⋊ C2×D11
HallC3×C5×C11 ⋊ C2×D17
HallC5×C17 ⋊ C2×C3×D11
HallC5×C11 ⋊ C2×C3×D17
HallC3×C17 ⋊ C2×C5×D11
HallC3×C11 ⋊ C2×C5×D17
SylowC17 ⋊ C2×C3×C5×D11
SylowC11 ⋊ C2×C3×C5×D17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5D187
commutator, cosocle, hypocenterC11×C17C22×C3×C5
FrattiniC1G
Fitting, socleC2×C3×C5×C11×C17C2
LCSG ▷ C11×C17
UCSC1 ◁ C2×C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2850 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C9×D187, C3×C5×D3×D187, C2×C32×C5×D187, …
maximal normal subgroup ofC2×C5×C9×D187, C2×C32×C5×D187
maximal quotient ofC2×C5×C9×D187, C3×C5×D3×D187, C2×C32×C5×D187, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11220, 118);