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C2×C11×D7×C17 #19104995

order5236
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C22×C11×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C11×D7×C17
unambiguous semidirect productC7⋊(C22×C11×C17)
unambiguous semidirect product(C2×C7)⋊(C2×C11×C17)

Splittings

Fitting, socleC2×C7×C11×C17 ⋊ C2
derived, SylowC7 ⋊ C22×C11×C17
HallC7×C11×C17 ⋊ C22
HallC7×C17 ⋊ C22×C11
HallC7×C11 ⋊ C22×C17

Subgroups

subgroupG/H
center, hypercenterC2×C11×C17D7
commutator, hypocenterC7C22×C11×C17
FrattiniC1G
Fitting, socleC2×C7×C11×C17C2
LCSG ▷ C7
UCSC1 ◁ C2×C11×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1870 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C11×C17×AGL(1,𝔽7), D3×C11×D7×C17, C2×C11×C17×D21, …
maximal normal subgroup ofC2×C11×C17×AGL(1,𝔽7), C2×C3×C11×D7×C17, C2×D7×C17×C11⋊C5, …
maximal quotient ofD3×C11×D7×C17, C2×C11×C17×D21, C2×C3×C11×D7×C17, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5236, 24);