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#10587720⋊D5 #19129761

order5460
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product#10587720⋊D5

Splittings

Fitting, socle, derived, HallC5×C7×C13 ⋊ C22×C3
HallD7×D65 ⋊ C3
HallC5×#63270 ⋊ C22
Hall#63270 ⋊ C2×D5
HallC7×C13 ⋊ C2×C3×D5
HallC5×C13 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×D13⋊C3
SylowC13 ⋊ D5×AGL(1,𝔽7)
SylowC7 ⋊ C2×C5⋊(D13⋊C3)
SylowC5 ⋊ #10587716⋊C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,3,5,7,13|d^a=d^4,f^a=f^12,e^b=e^6,e^c=e^2,f^c=f^3

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×C5⋊(D13⋊C3), C3×#10587720⋊D5, #10587720⋊D15, …
maximal normal subgroup ofAGL(1,𝔽7)×C5⋊(D13⋊C3), C3×#10587720⋊D5, C5×#10587720⋊D5, …
maximal quotient of#13109900⋊D5, C3×#10587720⋊D5, #10587720⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(5460, 103);