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(C13⋊C3)⋊D7 #10587714

order546
isoclinismisoclinic class of (C13⋊C3)⋊D7
automorphism?
homologyAbelianization (H1) = C2×C3 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product(C13⋊C3)⋊D7

Splittings

Fitting, socle, derived, HallC7×C13 ⋊ C2×C3
HallC7×C13⋊C3 ⋊ C2
HallD91 ⋊ C3
HallC13⋊C3 ⋊ D7
SylowC13 ⋊ C3×D7
SylowC7 ⋊ D13⋊C3

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC7×C13C2×C3
LCSG ▷ C7×C13
UCSC1

16 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 91

Polycyclic presentation:

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

Conjugacy classes & character table

29 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofD7×D13⋊C3, C2×(C13⋊C3)⋊D7, ΓL(1,𝔽8)⋊(D13⋊C3), …
maximal normal subgroup ofD7×D13⋊C3, C2×(C13⋊C3)⋊D7, ΓL(1,𝔽8)⋊(D13⋊C3), …
maximal quotient of#11763955, C2×(C13⋊C3)⋊D7, (C13⋊C9)⋊D7, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(546, 3);