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(C13⋊C3)⋊(C7⋊D7) #16838484

order3822
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C7

Aliases

unambiguous semidirect product(C13⋊C3)⋊(C7⋊D7)

Splittings

Fitting, socle, derived, HallC72×C13 ⋊ C2×C3
HallC72×C13⋊C3 ⋊ C2
HallC7⋊D91 ⋊ C3
SylowC72 ⋊ D13⋊C3
HallC13⋊C3 ⋊ C7⋊D7
SylowC13 ⋊ C3×C7⋊D7

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC72×C13C2×C3
LCSG ▷ C72×C13
UCSC1

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 637

Polycyclic presentation:

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

Conjugacy classes & character table

176 conjugacy classes — view the full character table.

Relationships

maximal subgroup of(C13⋊C3)⋊#64424, (C13⋊C3)⋊#64425, ΓL(1,𝔽8)⋊((C13⋊C3)⋊D7), …
maximal normal subgroup of(C13⋊C3)⋊#64424, (C13⋊C3)⋊#64425, ΓL(1,𝔽8)⋊((C13⋊C3)⋊D7), …
maximal quotient of(C13⋊C9)⋊(C7⋊D7), C3×(C13⋊C3)⋊(C7⋊D7), C3⋊((C13⋊C3)⋊(C7⋊D7)), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3822, 77);