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C5×C11⋊(Dic13⋊C3) #22575057

order8580
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11⋊(Dic13⋊C3)
unambiguous semidirect product(C5×Dic143)⋊C3

Splittings

derived, HallC11×C13 ⋊ C3×C4×C5
HallC5×Dic143 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C4
HallC5×C11×C13 ⋊ C3×C4
HallDic143 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C4×C5
HallC5×C13⋊C3 ⋊ Dic11
HallC5×C13 ⋊ C3×Dic11
HallC5×C11 ⋊ Dic13⋊C3
HallC13⋊C3 ⋊ C5×Dic11
SylowC13 ⋊ C3×C5×Dic11
SylowC11 ⋊ C5×Dic13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5C11⋊(D13⋊C3)
commutator, hypocenterC11×C13C3×C4×C5
FrattiniC2C5×C11⋊(D13⋊C3)
Fitting, socleC2×C5×C11×C13C2×C3
LCSG ▷ C11×C13
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

430 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C5×C11⋊(Dic13⋊C3), C5×C3⋊(C11⋊(Dic13⋊C3))
maximal normal subgroup ofC3×C5×C11⋊(Dic13⋊C3)
maximal quotient ofC5×C11⋊(Dic13⋊C9), C3×C5×C11⋊(Dic13⋊C3), C5×C3⋊(C11⋊(Dic13⋊C3))

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 29);