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D19⋊SL(2,𝔽3) #11744923

order912
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productD19⋊SL(2,𝔽3)

Splittings

Fitting, derivedQ8×C19 ⋊ C2×C3
HallQ8×D19 ⋊ C3
SylowC19 ⋊ C2×SL(2,𝔽3)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2D19⋊A4
commutator, Fitting, cosocle, hypocenterQ8×C19C2×C3
socleC2×C19C2×A4
LCSG ▷ Q8×C19
UCSC1 ◁ C2

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 152

Polycyclic presentation:

2,3,2^2,19,2|c^2=f,d^2=f,e^a=e^18,c^b=d,d^b=cdf,e^b=e^7,d^c=df

Conjugacy classes & character table

29 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×D19⋊SL(2,𝔽3), #14269884, D19⋊(#41⋊C3), …
maximal normal subgroup ofC2×D19⋊SL(2,𝔽3), #14269884, D19⋊(#41⋊C3), …
maximal quotient ofDic19⋊SL(2,𝔽3), C2×D19⋊SL(2,𝔽3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 134);