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C3×ΓL(1,𝔽8)×D115 #28408041

order14490
automorphism?
homologyAbelianization (H1) = C2×C32 · Schur multiplier (H2) = C3

Aliases

direct productC3×ΓL(1,𝔽8)×D115
unambiguous semidirect productC5⋊(C3×ΓL(1,𝔽8)×D23)
unambiguous semidirect productC23⋊(C3×D5×ΓL(1,𝔽8))
unambiguous semidirect product(C7×D115)⋊C32
unambiguous semidirect product(C3×C7×D115)⋊C3

Splittings

Fitting, socleC3×C5×C7×C23 ⋊ C2×C3
derived, HallC5×C7×C23 ⋊ C2×C32
HallC3×C5×ΓL(1,𝔽8)×C23 ⋊ C2
HallC7×D115 ⋊ C32
HallC3×ΓL(1,𝔽8)×C23 ⋊ D5
HallC3×C5×ΓL(1,𝔽8) ⋊ D23
HallC7×C23 ⋊ C32×D5
HallC5×C23 ⋊ C2×C3×ΓL(1,𝔽8)
HallC5×C7 ⋊ C32×D23
SylowC23 ⋊ C3×D5×ΓL(1,𝔽8)
SylowC7 ⋊ C32×D115
SylowC5 ⋊ C3×ΓL(1,𝔽8)×D23

Subgroups

subgroupG/H
center, hypercenterC3ΓL(1,𝔽8)×D115
commutator, cosocle, hypocenterC5×C7×C23C2×C32
FrattiniC1G
Fitting, socleC3×C5×C7×C23C2×C3
LCSG ▷ C5×C7×C23
UCSC1 ◁ C3

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2415

Conjugacy classes & character table

885 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×AGL(1,𝔽7)×D115, C3×(C5⋊AGL(1,𝔽7))⋊D23, C3×D5×ΓL(1,𝔽8)×D23, …
maximal normal subgroup ofC3×AGL(1,𝔽7)×D115, C3×(C5⋊AGL(1,𝔽7))⋊D23, C3×D5×ΓL(1,𝔽8)×D23, …
maximal quotient ofC3×ΓL(1,𝔽8)×Dic115, C2×C3×ΓL(1,𝔽8)×D115

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 32);