Finite Group Databasebeta

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C3⋊(C11⋊#10625194) #37567608

order24420
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C11⋊#10625194)
unambiguous semidirect productC11⋊(C3⋊#10625194)

Splittings

Fitting, socle, derived, HallC3×C5×C11×C37 ⋊ C4
HallC5×C11×C37 ⋊ Dic3
HallC3×C11×C37 ⋊ Dic5
HallC3×C5×C37 ⋊ Dic11
HallC11×C37 ⋊ Dic15
HallC5×C37 ⋊ Dic33
HallC3×C5×C11 ⋊ #3866
HallC3×C37 ⋊ Dic55
HallC5×C11 ⋊ C3⋊#3866
SylowC37 ⋊ Dic165
HallC3×C11 ⋊ #10625194
HallC3×C5 ⋊ C11⋊#3866
SylowC11 ⋊ C3⋊#10625194
SylowC5 ⋊ C3⋊(C11⋊#3866)
SylowC3 ⋊ C11⋊#10625194

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C11×C37C4
prime radical, cosocleC3×C5×C11×D37C2
LCSG ▷ C3×C5×C11×C37
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Polycyclic presentation:

2^2,3,5,11,37|a^2=b,c^a=c^2,d^a=d^4,e^a=e^10,f^a=f^31,f^b=f^36

Conjugacy classes & character table

1653 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 129);