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C3×(C11⋊C5)⋊AGL(1,𝔽5) #15693146

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

Aliases

direct productC3×(C11⋊C5)⋊AGL(1,𝔽5)
unambiguous semidirect product(C11⋊C5)⋊(C3×AGL(1,𝔽5))
unambiguous semidirect product(C11⋊AGL(1,𝔽5))⋊(C3×C5)
unambiguous semidirect product(C3×C11⋊AGL(1,𝔽5))⋊C5

Splittings

Fitting, socleC3×C5×C11 ⋊ C4×C5
derivedC5×C11 ⋊ C3×C4×C5
HallC3×C5×C11⋊C5 ⋊ C4
HallC5×C11⋊C5 ⋊ C3×C4
HallC3×C11 ⋊ C5×AGL(1,𝔽5)
SylowC11 ⋊ C3×C5×AGL(1,𝔽5)

Subgroups

subgroupG/H
center, hypercenterC3(C11⋊C5)⋊AGL(1,𝔽5)
commutator, hypocenterC5×C11C3×C4×C5
FrattiniC1G
Fitting, socleC3×C5×C11C4×C5
prime radicalC3×D5×C11⋊C5C2
cosocleD5×C11C2×C3×C5
LCSG ▷ C5×C11
UCSC1 ◁ C3

52 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 19
transitive degreeμt(G) = 165

Conjugacy classes & character table

87 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)⋊((C11⋊C5)⋊AGL(1,𝔽5)), ΓL(1,𝔽8)×(C11⋊C5)⋊AGL(1,𝔽5), C3×C7×(C11⋊C5)⋊AGL(1,𝔽5), …
maximal normal subgroup ofC3×C7×(C11⋊C5)⋊AGL(1,𝔽5), C3×C11×(C11⋊C5)⋊AGL(1,𝔽5), C3×AGL(1,𝔽5)×AGL(1,𝔽11), …
maximal quotient ofΓL(1,𝔽8)⋊((C11⋊C5)⋊AGL(1,𝔽5)), ΓL(1,𝔽8)×(C11⋊C5)⋊AGL(1,𝔽5), C3×C7×(C11⋊C5)⋊AGL(1,𝔽5), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3300, 66);