Finite Group Databasebeta

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(C11⋊C5)⋊#10596874 #44568441

order32340
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊#10596874
unambiguous semidirect product(C11⋊#10596874)⋊C5

Splittings

derived, HallC72×C11 ⋊ C3×C4×C5
HallC7⋊(C7⋊(Dic11⋊C5)) ⋊ C3
HallC11⋊C5×#3861 ⋊ C4
HallC11⋊#10596874 ⋊ C5
HallC72×C11⋊C5 ⋊ C3×C4
HallC7⋊Dic77 ⋊ C3×C5
HallC11×#3861 ⋊ C4×C5
Hall#3861 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ #10596874
SylowC72 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C5×#10596874

Subgroups

subgroupG/H
center, Frattini, hypercenterC2(C11⋊C5)⋊#64424
commutator, hypocenterC72×C11C3×C4×C5
Fitting, socle, cosocleC2×C72×C11C2×C3×C5
prime radicalC2×C11⋊C5×#3861C2
LCSG ▷ C72×C11
UCSC1 ◁ C2

240 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2156

Polycyclic presentation:

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

Conjugacy classes & character table

178 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32340, 143);