D₁₃₀₂₇ #39907555

order	26054
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₃₀₂₇
unambiguous semidirect product	C₇⋊D₁₈₆₁
unambiguous semidirect product	C₁₈₆₁⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₁₈₆₁ ⋊ C₂
Sylow	C₁₈₆₁ ⋊ D₇
Sylow	C₇ ⋊ D₁₈₆₁

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₈₆₁	C₂
LCS	G ▷ C₇×C₁₈₆₁
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1868
transitive degree	μ_t(G) = 13027

A minimal faithful permutation representation — 2 generators on 1868 points:

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Polycyclic presentation:

2,7,1861|b^a=b^6,c^a=c^1860

Conjugacy classes & character table

6515 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₃₀₂₇
maximal normal subgroup of	C₂×D₁₃₀₂₇
maximal quotient of	Dic₁₃₀₂₇, C₂×D₁₃₀₂₇

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26054, 3);

D13027 #39907555