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(C11⋊C5)⋊#90866 #38788019

order25740
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C3

Aliases

unambiguous semidirect product(C11⋊C5)⋊#90866
unambiguous semidirect product(C11⋊#90866)⋊C5

Splittings

Fitting, socle, derived, HallC32×C11×C13 ⋊ C4×C5
HallC32×C13×C11⋊C5 ⋊ C4
HallC11⋊#90866 ⋊ C5
HallC13×C11⋊C5 ⋊ #157
HallC32×C11⋊C5 ⋊ #261
HallC11×C13 ⋊ C5×#157
HallC32×C13 ⋊ Dic11⋊C5
HallC32×C11 ⋊ C5×#261
HallC11⋊C5 ⋊ #90866
SylowC13 ⋊ (C11⋊C5)⋊#157
SylowC11 ⋊ C5×#90866
SylowC32 ⋊ (C11⋊C5)⋊#261

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC32×C11×C13C4×C5
prime radicalC11⋊C5×C3⋊D39C2
cosocleC11×C3⋊D39C2×C5
LCSG ▷ C32×C11×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 858

Polycyclic presentation:

2,5,2,3^2,11,13|a^2=c,d^a=de,e^a=de^2,f^a=f^10,g^a=g^5,f^b=f^4,d^c=d^2,e^c=e^2,g^c=g^12

Conjugacy classes & character table

225 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25740, 250);