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C2×C7×D187 #19104996

order5236
isoclinismisoclinic class of D187
automorphism?
homologyAbelianization (H1) = C22×C7 · Schur multiplier (H2) = C2

Aliases

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

Splittings

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

Subgroups

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

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×ΓL(1,𝔽8)×D187, D3×C7×D187, C2×C7×D561, …
maximal normal subgroup ofC2×ΓL(1,𝔽8)×D187, C2×C3×C7×D187, C2×C7×C17⋊AGL(1,𝔽11), …
maximal quotient ofD3×C7×D187, C2×C7×D561, C2×C3×C7×D187, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5236, 25);