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D35⋊D73 #23779373

order10220
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productD35⋊D73
unambiguous semidirect productD365⋊D7
unambiguous semidirect productD511⋊D5

Splittings

Fitting, socle, derived, HallC5×C7×C73 ⋊ C22
HallC7×C73 ⋊ C2×D5
HallC5×C73 ⋊ C2×D7
SylowC73 ⋊ D5×D7
HallC5×C7 ⋊ C2×D73
SylowC7 ⋊ D5×D73
SylowC5 ⋊ D7×D73

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC5×C7×C73C22
LCSG ▷ C5×C7×C73
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,5,7,73|d^a=d^6,e^a=e^72,c^b=c^4,d^b=d^6

Conjugacy classes & character table

704 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#15690449⋊D5, #15690450⋊D5, (C5⋊AGL(1,𝔽7))⋊D73, …
maximal normal subgroup of#15690449⋊D5, #15690450⋊D5, (C5⋊AGL(1,𝔽7))⋊D73, …
maximal quotient ofC3×D35⋊D73, D511⋊D15, D365⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10220, 28);