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C3⋊(C11⋊#63118) #22575157

order8580
automorphism?
homologyAbelianization (H1) = C4 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect productC3⋊(C11⋊#63118)
unambiguous semidirect productC11⋊(C3⋊#63118)

Splittings

Fitting, socle, derived, HallC3×C5×C11×C13 ⋊ C4
HallC5×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ Dic5
HallC3×C5×C13 ⋊ Dic11
HallC3×C5×C11 ⋊ #261
HallC11×C13 ⋊ Dic15
HallC5×C13 ⋊ Dic33
HallC5×C11 ⋊ C3⋊#261
HallC3×C13 ⋊ Dic55
HallC3×C11 ⋊ #63118
HallC3×C5 ⋊ C11⋊#261
SylowC13 ⋊ Dic165
SylowC11 ⋊ C3⋊#63118
SylowC5 ⋊ C3⋊(C11⋊#261)
SylowC3 ⋊ C11⋊#63118

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC3×C5×C11×C13C4
LCSG ▷ C3×C5×C11×C13
UCSC1

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

663 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9⋊(C11⋊#63118), C3⋊(C11⋊(#63118⋊C3)), C3×C3⋊(C11⋊#63118), …
maximal normal subgroup ofC3⋊(C11⋊(#63118⋊C3)), C3×C3⋊(C11⋊#63118)
maximal quotient ofC9⋊(C11⋊#63118), C3×C3⋊(C11⋊#63118), C3⋊(C3⋊(C11⋊#63118))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 129);