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D5×ΓL(1,𝔽8)×C29 #20259043

order6090
automorphism?
homologyAbelianization (H1) = C2×C3×C29 · Schur multiplier (H2) = C1

Aliases

direct productD5×ΓL(1,𝔽8)×C29
unambiguous semidirect productC5⋊(C2×ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C7×D5)⋊(C3×C29)
unambiguous semidirect product(C7×D5×C29)⋊C3

Splittings

Fitting, socle, HallC5×C7×C29 ⋊ C2×C3
derived, HallC5×C7 ⋊ C2×C3×C29
HallC5×ΓL(1,𝔽8)×C29 ⋊ C2
HallC7×D5×C29 ⋊ C3
HallC7×C29 ⋊ C3×D5
HallC5×C29 ⋊ C2×ΓL(1,𝔽8)
HallC5×ΓL(1,𝔽8) ⋊ C2×C29
HallC7×D5 ⋊ C3×C29
SylowC7 ⋊ C3×D5×C29
SylowC5 ⋊ C2×ΓL(1,𝔽8)×C29

Subgroups

subgroupG/H
center, hypercenterC29D5×ΓL(1,𝔽8)
commutator, hypocenterC5×C7C2×C3×C29
FrattiniC1G
Fitting, socleC5×C7×C29C2×C3
LCSG ▷ C5×C7
UCSC1 ◁ C29

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

580 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC3×D5×ΓL(1,𝔽8)×C29, ΓL(1,𝔽8)×C29×D15, ΓL(1,𝔽8)×C29×D25, …
maximal normal subgroup ofC3×D5×ΓL(1,𝔽8)×C29, C5×D5×ΓL(1,𝔽8)×C29
maximal quotient ofD5×C29×C7⋊C9, C3×D5×ΓL(1,𝔽8)×C29, ΓL(1,𝔽8)×C29×D15, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6090, 29);