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C5×ΓL(1,𝔽8)×D39 #22551265

order8190
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×ΓL(1,𝔽8)×D39
unambiguous semidirect productC3⋊(C5×ΓL(1,𝔽8)×D13)

Splittings

Fitting, socleC3×C5×C7×C13 ⋊ C2×C3
derivedC3×C7×C13 ⋊ C2×C3×C5
HallC3×C5×C13×ΓL(1,𝔽8) ⋊ C2
HallC3×C13×ΓL(1,𝔽8) ⋊ C2×C5
HallC5×C7×C13 ⋊ C3×D3
HallC3×C5×ΓL(1,𝔽8) ⋊ D13
HallC7×C13 ⋊ C3×C5×D3
HallC5×C13 ⋊ D3×ΓL(1,𝔽8)
HallC3×ΓL(1,𝔽8) ⋊ C5×D13
HallC5×C7 ⋊ C3×D39
SylowC13 ⋊ C5×D3×ΓL(1,𝔽8)
SylowC7 ⋊ C3×C5×D39

Subgroups

subgroupG/H
center, hypercenterC5ΓL(1,𝔽8)×D39
commutator, hypocenterC3×C7×C13C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C7×C13C2×C3
LCSG ▷ C3×C7×C13
UCSC1 ◁ C5

72 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

525 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC5×AGL(1,𝔽7)×D39, C5×(C3⋊AGL(1,𝔽7))⋊D13, C5×D3×ΓL(1,𝔽8)×D13, …
maximal normal subgroup ofC5×AGL(1,𝔽7)×D39, C5×(C3⋊AGL(1,𝔽7))⋊D13, C5×D3×ΓL(1,𝔽8)×D13, …
maximal quotient ofC5×ΓL(1,𝔽8)×Dic39, C2×C5×ΓL(1,𝔽8)×D39

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8190, 99);