Finite Group Databasebeta

← Prev (#15693121) Next (#15693123) →

C3×(C11⋊C5)⋊Dic5 #15693122

order3300
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×(C11⋊C5)⋊Dic5
unambiguous semidirect product(C11⋊C5)⋊(C3×Dic5)
unambiguous semidirect productDic55⋊(C3×C5)
unambiguous semidirect product(C3×Dic55)⋊C5

Splittings

derivedC5×C11 ⋊ C3×C4×C5
HallC3×C5×C11⋊C5 ⋊ C4
HallC5×C11⋊C5 ⋊ C3×C4
HallC3×C11 ⋊ C5×Dic5
SylowC11 ⋊ C3×C5×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊AGL(1,𝔽11)
commutator, hypocenterC5×C11C3×C4×C5
FrattiniC2C3×C5⋊AGL(1,𝔽11)
Fitting, socleC2×C3×C5×C11C2×C5
prime radicalC2×C3×C5×C11⋊C5C2
cosocleC2×C5×C11C2×C3×C5
LCSG ▷ C5×C11
UCSC1 ◁ C2×C3

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 660

Conjugacy classes & character table

150 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)⋊((C11⋊C5)⋊Dic5), ΓL(1,𝔽8)×(C11⋊C5)⋊Dic5, C3×C7×(C11⋊C5)⋊Dic5, …
maximal normal subgroup ofC3×C7×(C11⋊C5)⋊Dic5, C3×C11×(C11⋊C5)⋊Dic5
maximal quotient ofΓL(1,𝔽8)⋊((C11⋊C5)⋊Dic5), ΓL(1,𝔽8)×(C11⋊C5)⋊Dic5, C3×C7×(C11⋊C5)⋊Dic5, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 42);