Finite Group Databasebeta

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C3⋊(C7⋊(C11⋊#1039)) #37528385

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

Aliases

unambiguous semidirect productC3⋊(C7⋊(C11⋊#1039))
unambiguous semidirect productC7⋊(C3⋊(C11⋊#1039))
unambiguous semidirect productC11⋊(C3⋊(C7⋊#1039))

Splittings

derived, HallC3×C52×C7×C11 ⋊ C4
HallC52×C7×C11 ⋊ Dic3
HallC3×C52×C11 ⋊ Dic7
HallC3×C52×C7 ⋊ Dic11
HallC52×C11 ⋊ Dic21
HallC3×C7×C11 ⋊ #1039
HallC52×C7 ⋊ Dic33
HallC7×C11 ⋊ C3⋊#1039
HallC3×C52 ⋊ Dic77
HallC3×C11 ⋊ C7⋊#1039
SylowC52 ⋊ Dic231
HallC3×C7 ⋊ C11⋊#1039
SylowC11 ⋊ C3⋊(C7⋊#1039)
SylowC7 ⋊ C3⋊(C11⋊#1039)
SylowC3 ⋊ C7⋊(C11⋊#1039)

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C3⋊(C5⋊D385)
commutator, hypocenterC3×C52×C7×C11C4
Fitting, socle, prime radical, cosocleC2×C3×C52×C7×C11C2
LCSG ▷ C3×C52×C7×C11
UCSC1 ◁ C2

192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 23100

Polycyclic presentation:

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

Conjugacy classes & character table

5778 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23100, 196);