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C3×(C11⋊C5)⋊Dic13 #22575050

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

Aliases

direct productC3×(C11⋊C5)⋊Dic13
unambiguous semidirect product(C11⋊C5)⋊(C3×Dic13)
unambiguous semidirect product(C3×Dic143)⋊C5

Splittings

derived, HallC11×C13 ⋊ C3×C4×C5
HallC3×C13×C11⋊C5 ⋊ C4
HallC3×Dic143 ⋊ C5
HallC13×C11⋊C5 ⋊ C3×C4
HallDic143 ⋊ C3×C5
HallC3×C11×C13 ⋊ C4×C5
HallC3×C11⋊C5 ⋊ Dic13
HallC11⋊C5 ⋊ C3×Dic13
HallC3×C13 ⋊ Dic11⋊C5
HallC3×C11 ⋊ C5×Dic13
SylowC13 ⋊ C3×Dic11⋊C5
SylowC11 ⋊ C3×C5×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3C13⋊AGL(1,𝔽11)
commutator, hypocenterC11×C13C3×C4×C5
FrattiniC2C3×C13⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C11×C13C2×C5
LCSG ▷ C11×C13
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

318 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC9×(C11⋊C5)⋊Dic13, (C11⋊C5)⋊(Dic13⋊C9), C3×(C11⋊C5)⋊(Dic13⋊C3), …
maximal normal subgroup ofC9×(C11⋊C5)⋊Dic13, (C11⋊C5)⋊(Dic13⋊C9), C3×(C11⋊C5)⋊(Dic13⋊C3), …
maximal quotient ofC9×(C11⋊C5)⋊Dic13, C32×(C11⋊C5)⋊Dic13, C3×C3⋊((C11⋊C5)⋊Dic13)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8580, 22);