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#11716321⋊C2 #13097604

order1596
isoclinismisoclinic class of #11716321⋊C2
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect product#11716321⋊C2
unambiguous semidirect product#11716325⋊C2
unambiguous semidirect product#11716327⋊C2

Splittings

Fitting, socle, derived, HallC7×C19 ⋊ C22×C3
HallD7×D19 ⋊ C3
Hall#87704 ⋊ C22
SylowC19 ⋊ C2×AGL(1,𝔽7)
SylowC7 ⋊ C2×D19⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C19C22×C3
LCSG ▷ C7×C19
UCSC1

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 26
transitive degreeμt(G) = 133

Polycyclic presentation:

2^2,3,7,19|e^a=e^18,d^b=d^6,d^c=d^4,e^c=e^11

Conjugacy classes & character table

29 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽7)×D19⋊C3, C3×#11716321⋊C2, #11716321⋊D3, …
maximal normal subgroup ofAGL(1,𝔽7)×D19⋊C3, C3×#11716321⋊C2, C7×#11716321⋊C2, …
maximal quotient of#14558780⋊C2, C3×#11716321⋊C2, #11716321⋊D3, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1596, 27);