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C4⋊(#1039⋊C5) #14522187

order2000
automorphism?
homologyAbelianization (H1) = C2×C4×C5 · Schur multiplier (H2) = C2×C5

Aliases

unambiguous semidirect productC4⋊(#1039⋊C5)
unambiguous semidirect product(C4⋊#1039)⋊C5

Splittings

SylowH(3,𝔽5) ⋊ C4⋊C4

Subgroups

subgroupG/H
centerC22C2×(C5⋊D5)⋊C5
commutatorC2×C52C2×C4×C5
Frattini, socleC22×C5C2×C5×D5
FittingC2×C4×H(3,𝔽5)C2
prime radicalC22×H(3,𝔽5)C22
cosocleC22×C52C22×C5
hypercenterC2×C4(C5⋊D5)⋊C5
hypocenterC52C5×C4⋊C4
LCSG ▷ C2×C52 ▷ C52
UCSC1 ◁ C22 ◁ C2×C4

123 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 400

Polycyclic presentation:

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

Conjugacy classes & character table

146 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2000, 150);