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C2×C17×D77 #19104993

order5236
isoclinismisoclinic class of D77
automorphism?
homologyAbelianization (H1) = C22×C17 · Schur multiplier (H2) = C2

Aliases

direct productC2×C17×D77
unambiguous semidirect product(C2×C7)⋊(C17×D11)
unambiguous semidirect product(C2×C11)⋊(D7×C17)

Splittings

Fitting, socleC2×C7×C11×C17 ⋊ C2
derived, HallC7×C11 ⋊ C22×C17
HallC7×C11×C17 ⋊ C22
HallC11×C17 ⋊ C2×D7
HallC7×C17 ⋊ C2×D11
SylowC11 ⋊ C2×D7×C17
SylowC7 ⋊ C2×C17×D11

Subgroups

subgroupG/H
center, hypercenterC2×C17D77
commutator, hypocenterC7×C11C22×C17
FrattiniC1G
Fitting, socleC2×C7×C11×C17C2
LCSG ▷ C7×C11
UCSC1 ◁ C2×C17

40 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1360 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C17×C11⋊AGL(1,𝔽7), D3×C17×D77, C2×C17×D231, …
maximal normal subgroup ofC2×C17×C11⋊AGL(1,𝔽7), C2×C3×C17×D77, C2×C17×C7⋊AGL(1,𝔽11), …
maximal quotient ofD3×C17×D77, C2×C17×D231, C2×C3×C17×D77, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5236, 22);