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#10587717⋊D7 #21439650

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

Aliases

unambiguous semidirect product#10587717⋊D7

Splittings

Fitting, socle, derived, HallC72×C13 ⋊ C22×C3
HallD13×C7⋊D7 ⋊ C3
HallC7×#63271 ⋊ C22
SylowC72 ⋊ C2×D13⋊C3
SylowC13 ⋊ C2×ΓL(1,𝔽8)⋊D7

Subgroups

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

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

2^2,3,7^2,13|f^a=f^12,d^b=d^6,e^b=e^6,d^c=d^2,f^c=f^9

Conjugacy classes & character table

96 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD13⋊C3×ΓL(1,𝔽8)⋊D7, #37524911, #37524912, …
maximal normal subgroup ofD13⋊C3×ΓL(1,𝔽8)⋊D7, #37524911, #37524912, …
maximal quotient of#13109897⋊D7, C3×#10587717⋊D7, #10587717⋊D21, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 219);