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C2×C5×ΓL(1,𝔽8)×C29 #20259017

order6090
isoclinismisoclinic class of ΓL(1,𝔽8)
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C29 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×ΓL(1,𝔽8)×C29
unambiguous semidirect product(C2×C7)⋊(C3×C5×C29)
unambiguous semidirect product(C2×C5×C7)⋊(C3×C29)
unambiguous semidirect product(C2×C7×C29)⋊(C3×C5)
unambiguous semidirect product(C2×C5×C7×C29)⋊C3

Splittings

Fitting, socle, HallC2×C5×C7×C29 ⋊ C3
derived, SylowC7 ⋊ C2×C3×C5×C29
HallC5×C7×C29 ⋊ C2×C3
HallC2×C7×C29 ⋊ C3×C5
HallC7×C29 ⋊ C2×C3×C5
HallC2×C5×C7 ⋊ C3×C29
HallC5×C7 ⋊ C2×C3×C29
HallC2×C7 ⋊ C3×C5×C29

Subgroups

subgroupG/H
center, hypercenterC2×C5×C29ΓL(1,𝔽8)
commutator, hypocenterC7C2×C3×C5×C29
FrattiniC1G
Fitting, socleC2×C5×C7×C29C3
LCSG ▷ C7
UCSC1 ◁ C2×C5×C29

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1450 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×ΓL(1,𝔽8)×C29, C2×C3×C5×ΓL(1,𝔽8)×C29, C2×ΓL(1,𝔽8)×C25×C29, …
maximal normal subgroup ofC2×C3×C5×ΓL(1,𝔽8)×C29, C2×ΓL(1,𝔽8)×C25×C29, C2×C52×ΓL(1,𝔽8)×C29
maximal quotient ofC2×C5×C29×C7⋊C9, C5×D3×ΓL(1,𝔽8)×C29, C2×C3×C5×ΓL(1,𝔽8)×C29, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6090, 3);