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(C11⋊C5)⋊(Dic37⋊C3) #37567515

order24420
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C11⋊C5)⋊(Dic37⋊C3)
unambiguous semidirect product(C11⋊(Dic37⋊C3))⋊C5
unambiguous semidirect product((C11⋊C5)⋊Dic37)⋊C3

Splittings

derived, HallC11×C37 ⋊ C3×C4×C5
Hall(C11⋊C5)⋊Dic37 ⋊ C3
HallC11⋊C5×C37⋊C3 ⋊ C4
HallC11⋊(Dic37⋊C3) ⋊ C5
HallC37×C11⋊C5 ⋊ C3×C4
HallDic407 ⋊ C3×C5
HallC11×C37⋊C3 ⋊ C4×C5
HallC37⋊C3 ⋊ Dic11⋊C5
HallC11⋊C5 ⋊ Dic37⋊C3
SylowC37 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C5×Dic37⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2(C11⋊C5)⋊(D37⋊C3)
commutator, hypocenterC11×C37C3×C4×C5
Fitting, socle, cosocleC2×C11×C37C2×C3×C5
prime radicalC2×C11⋊C5×C37⋊C3C2
LCSG ▷ C11×C37
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1628

Polycyclic presentation:

2,3,5,11,37,2|a^2=f,d^a=d^10,e^a=e^36,e^b=e^26,d^c=d^4

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 36);