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C2×C7×ΓL(1,𝔽8)×D13 #21439698

order7644
automorphism?
homologyAbelianization (H1) = C22×C3×C7 · Schur multiplier (H2) = C2

Aliases

direct productC2×C7×ΓL(1,𝔽8)×D13

Splittings

Fitting, socleC2×C72×C13 ⋊ C2×C3
derivedC7×C13 ⋊ C22×C3×C7
HallC2×C72×D13 ⋊ C3
HallC7×C13×ΓL(1,𝔽8) ⋊ C22
HallC72×C13 ⋊ C22×C3
SylowC72 ⋊ C2×C3×D13
SylowC13 ⋊ C22×C7×ΓL(1,𝔽8)

Subgroups

subgroupG/H
center, hypercenterC2×C7ΓL(1,𝔽8)×D13
commutator, hypocenterC7×C13C22×C3×C7
FrattiniC1G
Fitting, socleC2×C72×C13C2×C3
LCSG ▷ C7×C13
UCSC1 ◁ C2×C7

100 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

560 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C7×ΓL(1,𝔽8)×D13⋊C3, C2×ΓL(1,𝔽8)×#10587716, C2×ΓL(1,𝔽8)×#10587717, …
maximal normal subgroup ofC2×C7×ΓL(1,𝔽8)×D13⋊C3, C2×ΓL(1,𝔽8)×#10587716, C2×ΓL(1,𝔽8)×#10587717, …
maximal quotient ofC2×C7×D13×C7⋊C9, D3×C7×ΓL(1,𝔽8)×D13, C2×C3×C7×ΓL(1,𝔽8)×D13, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 267);