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C3⋊#10619372 #14514338

order1920
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊#10619372

Splittings

SylowC3 ⋊ #10619372

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊#66297
commutator, prime radical, hypocenterC3×2−1+4⋊C5C4
FittingC3×2−1+4AGL(1,𝔽5)
socleC2×C3#66297
cosocleC3×#66243C2
LCSG ▷ C3×2−1+4⋊C5
UCSC1 ◁ C2

92 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 83
transitive degreeμt(G) = 240

Polycyclic presentation:

2^2,3,5,2^5|a^2=b,b^2=i,f^2=i,g^2=i,c^a=c^2,d^a=d^2,e^a=egi,f^a=fhi,g^a=fgh,h^a=hi,d^b=d^4,e^b=efh,f^b=fi,g^b=ghi,e^d=efgi,f^d=ef,g^d=gh,h^d=eg,g^e=gi,h^e=hi,g^f=gi

Conjugacy classes & character table

30 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1920, 240036);