Finite Group Databasebeta

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C3⋊((C11⋊C5)⋊#5997) #44568591

order32340
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C7

Aliases

unambiguous semidirect productC3⋊((C11⋊C5)⋊#5997)
unambiguous semidirect product(C11⋊C5)⋊(C3⋊#5997)
unambiguous semidirect product(C3⋊(C11⋊#5997))⋊C5

Splittings

Fitting, socle, derived, HallC3×C72×C11 ⋊ C4×C5
HallC3×C72×C11⋊C5 ⋊ C4
HallC3⋊(C11⋊#5997) ⋊ C5
HallC72×C11⋊C5 ⋊ Dic3
HallC72×C11 ⋊ C5×Dic3
HallC3×C11⋊C5 ⋊ #5997
HallC3×C72 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ C3⋊#5997
SylowC72 ⋊ C3⋊(Dic11⋊C5)
HallC3×C11 ⋊ C5×#5997
SylowC11 ⋊ C5×C3⋊#5997
SylowC3 ⋊ (C11⋊C5)⋊#5997

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C72×C11C4×C5
prime radicalC3×C11⋊C5×C7⋊D7C2
cosocleC3×C11×C7⋊D7C2×C5
LCSG ▷ C3×C72×C11
UCSC1

112 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Polycyclic presentation:

2,5,2,3,7^2,11|a^2=c,d^a=d^2,e^a=e^4f^3,f^a=e^6f^3,g^a=g^10,g^b=g^4,e^c=e^6,f^c=f^6

Conjugacy classes & character table

288 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 293);