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C2×D3×ΓL(1,𝔽8)×C29 #20300640

order7308
automorphism?
homologyAbelianization (H1) = C22×C3×C29 · Schur multiplier (H2) = C2

Aliases

direct productC2×D3×ΓL(1,𝔽8)×C29
unambiguous semidirect productC3⋊(C22×ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C2×C3)⋊(C2×ΓL(1,𝔽8)×C29)
unambiguous semidirect product(C2×D3×C7)⋊(C3×C29)
unambiguous semidirect product(C2×D3×C7×C29)⋊C3

Splittings

Fitting, socleC2×C3×C7×C29 ⋊ C2×C3
derivedC3×C7 ⋊ C22×C3×C29
HallC3×ΓL(1,𝔽8)×C29 ⋊ C22
HallC7×C29 ⋊ C2×C3×D3
HallC3×ΓL(1,𝔽8) ⋊ C22×C29
SylowC7 ⋊ C2×C3×D3×C29

Subgroups

subgroupG/H
center, hypercenterC2×C29D3×ΓL(1,𝔽8)
commutator, hypocenterC3×C7C22×C3×C29
FrattiniC1G
Fitting, socleC2×C3×C7×C29C2×C3
LCSG ▷ C3×C7
UCSC1 ◁ C2×C29

88 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

870 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD3×D5×ΓL(1,𝔽8)×C29, C2×C5×D3×ΓL(1,𝔽8)×C29, C2×ΓL(1,𝔽8)×C29×D15
maximal normal subgroup ofC2×C5×D3×ΓL(1,𝔽8)×C29
maximal quotient ofD3×D5×ΓL(1,𝔽8)×C29, C2×C5×D3×ΓL(1,𝔽8)×C29, C2×ΓL(1,𝔽8)×C29×D15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7308, 115);