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C11⋊C5×Dic13⋊C3 #22575062

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

Aliases

direct productC11⋊C5×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C11⋊C5)
unambiguous semidirect product(C11×Dic13⋊C3)⋊C5
unambiguous semidirect product(Dic13×C11⋊C5)⋊C3

Splittings

derived, HallC11×C13 ⋊ C3×C4×C5
HallDic13×C11⋊C5 ⋊ C3
HallC13⋊C3×C11⋊C5 ⋊ C4
HallC11×Dic13⋊C3 ⋊ C5
HallC13×C11⋊C5 ⋊ C3×C4
HallC11×Dic13 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C4×C5
HallDic13 ⋊ C3×C11⋊C5
HallC13⋊C3 ⋊ C4×C11⋊C5
SylowC13 ⋊ C3×C4×C11⋊C5
SylowC11 ⋊ C5×Dic13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC2C11⋊C5×D13⋊C3
commutator, hypocenterC11×C13C3×C4×C5
Fitting, socleC2×C11×C13C2×C3×C5
LCSG ▷ C11×C13
UCSC1 ◁ C2

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

112 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×C11⋊C5×Dic13⋊C3, C11⋊C5×C3⋊(Dic13⋊C3)
maximal normal subgroup ofC3×C11⋊C5×Dic13⋊C3
maximal quotient ofC11⋊C5×Dic13⋊C9, C3×C11⋊C5×Dic13⋊C3, C11⋊C5×C3⋊(Dic13⋊C3)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 34);