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C4⋊(C3⋊#1035) #11924905

order1200
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C2

Aliases

unambiguous semidirect productC4⋊(C3⋊#1035)

Splittings

FittingC3×C4×C25 ⋊ C4
HallC3×C25 ⋊ C4⋊C4
SylowC25 ⋊ C4⋊Dic3
SylowC3 ⋊ C4⋊#1035

Subgroups

subgroupG/H
centerC2C2×C3⋊#1035
commutatorC2×C3×C25C2×C4
FrattiniC2×C5C2×ΓL(1,𝔽16)
FittingC3×C4×C25C4
socleC2×C3×C5C2×AGL(1,𝔽5)
prime radical, cosocleC2×C3×D25C22
hypercenterC4C3⋊#1035
hypocenterC3×C25C4⋊C4
LCSG ▷ C2×C3×C25 ▷ C3×C25
UCSC1 ◁ C2 ◁ C4

78 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 300

Polycyclic presentation:

2^4,3,5^2|a^2=c,b^2=d,f^5=g,b^a=bd,e^a=e^2,f^a=f^2g,g^a=g^2,f^c=f^4g^4,g^c=g^4

Conjugacy classes & character table

90 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1200, 115);