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#64423⋊D13 #21439614

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

Aliases

unambiguous semidirect product#64423⋊D13

Splittings

Fitting, socle, derived, HallC72×C13 ⋊ C22×C3
HallD7×D91 ⋊ C3
HallC13×#3861 ⋊ C22
Hall#3861 ⋊ C2×D13
SylowC72 ⋊ C2×C3×D13
SylowC13 ⋊ #64423⋊C2

Subgroups

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

104 conjugacy classes of subgroups.

Full subgroup data →

Presentation

Polycyclic presentation:

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

Conjugacy classes & character table

121 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(#64418⋊C3)⋊D13, #37524926, #37524927, …
maximal normal subgroup of#37524926, #37524927, AGL(1,𝔽7)×ΓL(1,𝔽8)⋊D13, …
maximal quotient of#11725076⋊D13, C3×#64423⋊D13, #64423⋊D39, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7644, 183);