D₁₃₁₅₃ #39911554

order	26306
automorphism	?
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₁₃₁₅₃
unambiguous semidirect product	C₇⋊D₁₈₇₉
unambiguous semidirect product	C₁₈₇₉⋊D₇

Splittings

Fitting, socle, derived, Hall	C₇×C₁₈₇₉ ⋊ C₂
Sylow	C₁₈₇₉ ⋊ D₇
Sylow	C₇ ⋊ D₁₈₇₉

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₇×C₁₈₇₉	C₂
LCS	G ▷ C₇×C₁₈₇₉
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1886
transitive degree	μ_t(G) = 13153

A minimal faithful permutation representation — 2 generators on 1886 points:

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Polycyclic presentation:

2,7,1879|b^a=b^6,c^a=c^1878

Conjugacy classes & character table

6578 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×D₁₃₁₅₃
maximal normal subgroup of	C₂×D₁₃₁₅₃
maximal quotient of	Dic₁₃₁₅₃, C₂×D₁₃₁₅₃

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26306, 3);

D13153 #39911554