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C2×C13×#64424 #21439701

order7644
isoclinismisoclinic class of #64424
automorphism?
homologyAbelianization (H1) = C22×C3×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C13×#64424

Splittings

Fitting, socleC2×C72×C13 ⋊ C2×C3
derived, SylowC72 ⋊ C22×C3×C13
HallC2×C13×C7⋊D7 ⋊ C3
HallC13×#3861 ⋊ C22
HallC72×C13 ⋊ C22×C3
HallC2×C7⋊D7 ⋊ C3×C13
Hall#3861 ⋊ C22×C13

Subgroups

subgroupG/H
center, hypercenterC2×C13#64424
commutator, hypocenterC72C22×C3×C13
FrattiniC1G
Fitting, socleC2×C72×C13C2×C3
LCSG ▷ C72
UCSC1 ◁ C2×C13

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

364 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC2×C13×ΓL(1,𝔽8)⋊AGL(1,𝔽7), C2×#64424⋊(C13⋊C3), C2×C13⋊C3×#64424, …
maximal normal subgroup ofC2×C13×ΓL(1,𝔽8)⋊AGL(1,𝔽7), C2×#64424⋊(C13⋊C3), C2×C13⋊C3×#64424, …
maximal quotient ofC2×C13×#11725077, D3×C13×#64424, C2×C3×C13×#64424, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 270);