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C3⋊(C3⋊#1043) #11744701

order900
isoclinismisoclinic class of C3⋊(C3⋊#1043)
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect productC3⋊(C3⋊#1043)

Splittings

Fitting, socle, derived, HallC32×C52 ⋊ C4
SylowC52 ⋊ C3⋊Dic3
SylowC32 ⋊ #1043

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C52C4
prime radical, cosocleC32×C5⋊D5C2
LCSG ▷ C32×C52
UCSC1

144 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 225

Polycyclic presentation:

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

Conjugacy classes & character table

66 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#14268408, C3⋊D3×#1043, D5⋊(C3⋊ΓL(1,𝔽16)), …
maximal normal subgroup of#14268408, C3⋊D3×#1043, D5⋊(C3⋊ΓL(1,𝔽16)), …
maximal quotient ofC3⋊(C3⋊#6033), C2×C3⋊(C3⋊#1043), C13×C3⋊(C3⋊#1043), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(900, 113);