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#11716321⋊D5 #22547646

order7980
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product#11716321⋊D5

Splittings

Fitting, socle, derived, HallC5×C7×C19 ⋊ C22×C3
HallD19×D35 ⋊ C3
HallC5×#87704 ⋊ C22
Hall#87704 ⋊ C2×D5
HallC7×C19 ⋊ C2×C3×D5
HallC5×C19 ⋊ C2×AGL(1,𝔽7)
HallC5×C7 ⋊ C2×D19⋊C3
SylowC19 ⋊ C2×C5⋊AGL(1,𝔽7)
SylowC7 ⋊ D5×D19⋊C3
SylowC5 ⋊ #11716321⋊C2

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC5×C7×C19C22×C3
LCSG ▷ C5×C7×C19
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,3,5,7,19|f^a=f^18,d^b=d^4,e^b=e^6,e^c=e^2,f^c=f^7

Conjugacy classes & character table

91 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD19⋊C3×C5⋊AGL(1,𝔽7), C3×#11716321⋊D5, #11716321⋊D15, …
maximal normal subgroup ofD19⋊C3×C5⋊AGL(1,𝔽7), C3×#11716321⋊D5
maximal quotient of#14558780⋊D5, C3×#11716321⋊D5, #11716321⋊D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 71);