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D13×#64422 #21439634

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

Aliases

direct productD13×#64422

Splittings

Fitting, socle, derived, HallC72×C13 ⋊ C22×C3
HallC7×D7×D13 ⋊ C3
HallC13×#3862 ⋊ C22
Hall#3862 ⋊ C2×D13
SylowC72 ⋊ C2×C3×D13
SylowC13 ⋊ C2×#64422

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC72×C13C22×C3
LCSG ▷ C72×C13
UCSC1

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#37524899, #37524900, ΓL(1,𝔽8)×D13×AGL(1,𝔽7), …
maximal normal subgroup of#37524899, #37524900, ΓL(1,𝔽8)×D13×AGL(1,𝔽7), …
maximal quotient ofD13×#11725075, C3×D13×#64422, D13×C3⋊#64422, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 203);