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D5×C7⋊AGL(1,𝔽11) #21440402

order7700
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productD5×C7⋊AGL(1,𝔽11)
unambiguous semidirect product(C7×D5)⋊AGL(1,𝔽11)
unambiguous semidirect product(D5×C11⋊C5)⋊D7
unambiguous semidirect product(D5×D77)⋊C5

Splittings

Fitting, socle, derivedC5×C7×C11 ⋊ C22×C5
HallC5×C7×C11⋊C5 ⋊ C22
HallC5×C11⋊C5 ⋊ C2×D7
HallC7×C11 ⋊ C2×C5×D5
SylowC11 ⋊ C5×D5×D7
SylowC7 ⋊ D5×AGL(1,𝔽11)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C11C22×C5
LCSG ▷ C5×C7×C11
UCSC1

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

128 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C3×D5×C7⋊AGL(1,𝔽11), D15×C7⋊AGL(1,𝔽11), …
maximal normal subgroup ofD5×ΓL(1,𝔽8)⋊AGL(1,𝔽11), C3×D5×C7⋊AGL(1,𝔽11)
maximal quotient ofC3×D5×C7⋊AGL(1,𝔽11), D15×C7⋊AGL(1,𝔽11), D5×C3⋊(C7⋊AGL(1,𝔽11)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 66);