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C19×SL(2,ℤ/4) #11744905

order912
isoclinismisoclinic class of S4
automorphism?
homologyAbelianization (H1) = C4×C19 · Schur multiplier (H2) = C2

Aliases

direct productC19×SL(2,ℤ/4)
unambiguous semidirect productA4⋊(C4×C19)

Splittings

derivedA4 ⋊ C4×C19

Subgroups

subgroupG/H
center, hypercenterC2×C19S4
commutator, hypocenterA4C4×C19
FrattiniC2C19×S4
Fitting, socleC23×C19D3
prime radicalC2×A4×C19C2
cosocleC2×A4C2×C19
LCSG ▷ A4
UCSC1 ◁ C2×C19

38 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 27
transitive degreeμt(G) = 228

A minimal faithful permutation representation — 2 generators on 27 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19)(20,21,22,23)(24,25,27,26);(25,26,27)

Conjugacy classes & character table

190 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14269824, (A4⋊D19)⋊C4, D19×SL(2,ℤ/4), …
maximal normal subgroup of#14269824, (A4⋊D19)⋊C4, D19×SL(2,ℤ/4), …
maximal quotient ofC19×A4⋊C8, C19×#859, C19×GU(2,𝔽3), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 116);