Finite Group Databasebeta

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C5×C11×Dic13⋊C3 #22575055

order8580
isoclinismisoclinic class of D13⋊C3
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×Dic13⋊C3
unambiguous semidirect productDic13⋊(C3×C5×C11)
unambiguous semidirect product(C5×Dic13)⋊(C3×C11)
unambiguous semidirect product(C5×C11×Dic13)⋊C3

Splittings

derived, SylowC13 ⋊ C3×C4×C5×C11
HallC5×C11×Dic13 ⋊ C3
HallC5×C11×C13⋊C3 ⋊ C4
HallC5×C11×C13 ⋊ C3×C4
HallC11×Dic13 ⋊ C3×C5
HallC11×C13⋊C3 ⋊ C4×C5
HallC5×Dic13 ⋊ C3×C11
HallC5×C13⋊C3 ⋊ C4×C11
HallC11×C13 ⋊ C3×C4×C5
HallC5×C13 ⋊ C3×C4×C11
HallDic13 ⋊ C3×C5×C11
HallC13⋊C3 ⋊ C4×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11D13⋊C3
commutator, hypocenterC13C3×C4×C5×C11
FrattiniC2C5×C11×D13⋊C3
Fitting, socleC2×C5×C11×C13C2×C3
LCSG ▷ C13
UCSC1 ◁ C2×C5×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

880 conjugacy classes — view the full character table.

Relationships

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 27);