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PSU(3,𝔽2)⋊D5 #10624312

order720
isoclinismisoclinic class of PSU(3,𝔽2)⋊D5
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productPSU(3,𝔽2)⋊D5

Splittings

Fitting, socle, HallC32×C5 ⋊ SD16
SylowC32 ⋊ #688
SylowC5 ⋊ AΓL(1,𝔽9)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, cosocleC5×#157C22
Fitting, socle, hypocenterC32×C5SD16
prime radical#157⋊D5C2
LCSG ▷ C5×#157 ▷ C5×C3⋊D3 ▷ C32×C5
UCSC1

50 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 45

Polycyclic presentation:

2^4,3^2,5|b^2=d,c^2=d,b^a=bc,c^a=cd,f^a=f^2,g^a=g^4,c^b=cd,e^b=ef,f^b=ef^2,e^c=f^2,f^c=e,e^d=e^2,f^d=f^2

Conjugacy classes & character table

21 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD5×AΓL(1,𝔽9), C2×PSU(3,𝔽2)⋊D5, #72213709, …
maximal normal subgroup ofD5×AΓL(1,𝔽9), C2×PSU(3,𝔽2)⋊D5, C3×PSU(3,𝔽2)⋊D5
maximal quotient of#13088396, PSU(3,𝔽2)⋊Dic5, #13088398, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(720, 781);