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D35⋊AGL(1,𝔽11) #21440403

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

Aliases

unambiguous semidirect productD35⋊AGL(1,𝔽11)
unambiguous semidirect product(C5⋊AGL(1,𝔽11))⋊D7
unambiguous semidirect product(C7⋊AGL(1,𝔽11))⋊D5
unambiguous semidirect product(D35⋊D11)⋊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 →

Presentation

Polycyclic presentation:

2^2,5^2,7,11|e^a=e^6,f^a=f^10,d^b=d^4,e^b=e^6,f^c=f^4

Conjugacy classes & character table

119 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C5⋊AGL(1,𝔽7))⋊AGL(1,𝔽11), C3×D35⋊AGL(1,𝔽11), (C7⋊AGL(1,𝔽11))⋊D15, …
maximal normal subgroup of(C5⋊AGL(1,𝔽7))⋊AGL(1,𝔽11), C3×D35⋊AGL(1,𝔽11)
maximal quotient ofC3×D35⋊AGL(1,𝔽11), (C7⋊AGL(1,𝔽11))⋊D15, (C5⋊AGL(1,𝔽11))⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 67);