D₅₄₆₉ #24926470

order	10938
automorphism	Aut(G) order 19929036
homology	Abelianization (H₁) = C₂ · Schur multiplier (H₂) = C₁

Aliases

dihedral	D₅₄₆₉
unambiguous semidirect product	C₃⋊D₁₈₂₃
unambiguous semidirect product	C₁₈₂₃⋊D₃

Splittings

Fitting, socle, derived, Hall	C₃×C₁₈₂₃ ⋊ C₂
Sylow	C₁₈₂₃ ⋊ D₃
Sylow	C₃ ⋊ D₁₈₂₃

Subgroups

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₃×C₁₈₂₃	C₂
LCS	G ▷ C₃×C₁₈₂₃
UCS	C₁

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 1826
transitive degree	μ_t(G) = 5469

A minimal faithful permutation representation — 2 generators on 1826 points:

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Polycyclic presentation:

2,3,1823|b^a=b^2,c^a=c^1822

Conjugacy classes & character table

2736 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	D₃×D₁₈₂₃, C₂×D₅₄₆₉, D₁₆₄₀₇, …
maximal normal subgroup of	D₃×D₁₈₂₃, C₂×D₅₄₆₉, C₃×D₅₄₆₉
maximal quotient of	Dic₅₄₆₉, C₂×D₅₄₆₉, D₁₆₄₀₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10938, 3);

D5469 #24926470