Finite Group Databasebeta

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C3⋊(C7⋊(C11⋊#1044)) #37528729

order23100
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C5

Aliases

unambiguous semidirect productC3⋊(C7⋊(C11⋊#1044))
unambiguous semidirect productC7⋊(C3⋊(C11⋊#1044))
unambiguous semidirect productC11⋊(C3⋊(C7⋊#1044))

Splittings

Fitting, socle, derived, HallC3×C52×C7×C11 ⋊ C4
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C11 ⋊ Dic7
HallC3×C52×C7 ⋊ Dic11
HallC52×C11 ⋊ Dic21
HallC3×C7×C11 ⋊ #1044
HallC52×C7 ⋊ Dic33
HallC7×C11 ⋊ C3⋊#1044
HallC3×C52 ⋊ Dic77
HallC3×C11 ⋊ C7⋊#1044
SylowC52 ⋊ Dic231
HallC3×C7 ⋊ C11⋊#1044
SylowC11 ⋊ C3⋊(C7⋊#1044)
SylowC7 ⋊ C3⋊(C11⋊#1044)
SylowC3 ⋊ C7⋊(C11⋊#1044)

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C52×C7×C11C4
prime radical, cosocleC3×C7×C11×C5⋊D5C2
LCSG ▷ C3×C52×C7×C11
UCSC1

128 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2310

Polycyclic presentation:

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

Conjugacy classes & character table

1620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 540);