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D35⋊D61 #22555424

order8540
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD35⋊D61
unambiguous semidirect productD305⋊D7
unambiguous semidirect productD427⋊D5

Splittings

Fitting, socle, derived, HallC5×C7×C61 ⋊ C22
HallC7×C61 ⋊ C2×D5
HallC5×C61 ⋊ C2×D7
SylowC61 ⋊ D5×D7
HallC5×C7 ⋊ C2×D61
SylowC7 ⋊ D5×D61
SylowC5 ⋊ D7×D61

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C61C22
LCSG ▷ C5×C7×C61
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,5,7,61|d^a=d^6,e^a=e^60,c^b=c^4,d^b=d^6

Conjugacy classes & character table

590 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14579429⋊D5, #14579428⋊D5, (C5⋊AGL(1,𝔽7))⋊D61, …
maximal normal subgroup of#14579429⋊D5, #14579428⋊D5, (C5⋊AGL(1,𝔽7))⋊D61, …
maximal quotient ofC3×D35⋊D61, D427⋊D15, D305⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8540, 39);