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C5×D3×ΓL(1,𝔽8)×C23 #28408044

order14490
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C23 · Schur multiplier (H2) = C1

Aliases

direct productC5×D3×ΓL(1,𝔽8)×C23
unambiguous semidirect productC3⋊(C2×C5×ΓL(1,𝔽8)×C23)
unambiguous semidirect product(D3×C7)⋊(C3×C5×C23)
unambiguous semidirect product(C5×D3×C7)⋊(C3×C23)
unambiguous semidirect product(D3×C7×C23)⋊(C3×C5)
unambiguous semidirect product(C5×D3×C7×C23)⋊C3

Splittings

Fitting, socleC3×C5×C7×C23 ⋊ C2×C3
derivedC3×C7 ⋊ C2×C3×C5×C23
HallC3×C5×ΓL(1,𝔽8)×C23 ⋊ C2
HallC3×ΓL(1,𝔽8)×C23 ⋊ C2×C5
HallC5×C7×C23 ⋊ C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ C2×C23
HallC7×C23 ⋊ C3×C5×D3
HallC3×ΓL(1,𝔽8) ⋊ C2×C5×C23
HallC5×C7 ⋊ C3×D3×C23
SylowC7 ⋊ C3×C5×D3×C23

Subgroups

subgroupG/H
center, hypercenterC5×C23D3×ΓL(1,𝔽8)
commutator, cosocle, hypocenterC3×C7C2×C3×C5×C23
FrattiniC1G
Fitting, socleC3×C5×C7×C23C2×C3
LCSG ▷ C3×C7
UCSC1 ◁ C5×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2415

Conjugacy classes & character table

1725 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C23×AGL(1,𝔽7), C5×D3×ΓL(1,𝔽8)⋊D23, C5×D3×ΓL(1,𝔽8)×D23, …
maximal normal subgroup ofC5×D3×C23×AGL(1,𝔽7), C5×D3×ΓL(1,𝔽8)⋊D23, C5×D3×ΓL(1,𝔽8)×D23, …
maximal quotient ofC5×Dic3×ΓL(1,𝔽8)×C23, C2×C5×D3×ΓL(1,𝔽8)×C23

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14490, 35);