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#14522232

order2000
automorphism?
homologyAbelianization (H1) = C2×C4 · Schur multiplier (H2) = C1

Aliases

No aliases for this group.

Splittings

SylowH(3,𝔽5) ⋊ M16

Subgroups

subgroupG/H
center, FrattiniC4×C5C2×C5⋊D5
commutatorC2×H(3,𝔽5)C2×C4
FittingC2×C4×H(3,𝔽5)C2
socleC2×C5C2×#1039
prime radicalC22×H(3,𝔽5)C4
cosocleC4×H(3,𝔽5)C22
hypercenterC2×C4×C5C5⋊D5
hypocenterH(3,𝔽5)M16
LCSG ▷ C2×H(3,𝔽5) ▷ H(3,𝔽5)
UCSC1 ◁ C4×C5 ◁ C2×C4×C5

150 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 200

Polycyclic presentation:

2^4,5^3|a^2=c,c^2=d,b^a=bd,e^a=e^4,f^a=f^4,f^e=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, 195);