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C3⋊GL(2,𝔽5) #13085369

order1440
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊GL(2,𝔽5)

Splittings

derivedC3×SL(2,𝔽5) ⋊ C4

Subgroups

subgroupG/H
center, Frattini, hypercenterC4ΓL(2,𝔽4)
commutator, hypocenterC3×SL(2,𝔽5)C4
FittingC3×C4S5
socleC2×C3A5⋊C4
prime radical, cosocleC3×#6732C2
LCSG ▷ C3×SL(2,𝔽5)
UCSC1 ◁ C4

106 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 72

Permutation generators:

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×GL(2,𝔽5), #72275838, C2×C3⋊GL(2,𝔽5), …
maximal normal subgroup ofD3×GL(2,𝔽5), C2×C3⋊GL(2,𝔽5)
maximal quotient of#72275838, C2×C3⋊GL(2,𝔽5)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1440, 1686);