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C2×C3×C7×D187 #30628181

order15708
isoclinismisoclinic class of D187
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3×C7×D187
unambiguous semidirect product(C2×C11)⋊(C3×C7×D17)
unambiguous semidirect product(C2×C17)⋊(C3×C7×D11)

Splittings

Fitting, socleC2×C3×C7×C11×C17 ⋊ C2
derived, HallC11×C17 ⋊ C22×C3×C7
HallC3×C7×C11×C17 ⋊ C22
HallC7×C11×C17 ⋊ C22×C3
HallC3×C11×C17 ⋊ C22×C7
HallC3×C7×C17 ⋊ C2×D11
HallC3×C7×C11 ⋊ C2×D17
HallC7×C17 ⋊ C2×C3×D11
HallC7×C11 ⋊ C2×C3×D17
HallC3×C17 ⋊ C2×C7×D11
HallC3×C11 ⋊ C2×C7×D17
SylowC17 ⋊ C2×C3×C7×D11
SylowC11 ⋊ C2×C3×C7×D17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D187
commutator, cosocle, hypocenterC11×C17C22×C3×C7
FrattiniC1G
Fitting, socleC2×C3×C7×C11×C17C2
LCSG ▷ C11×C17
UCSC1 ◁ C2×C3×C7

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7854

Conjugacy classes & character table

3990 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15708, 102);