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C₁₃×#6105 #72259246

order	2704
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃ · Schur multiplier (H₂) = C₁

Aliases

Splittings

C₁₃² ⋊ SD₁₆

Subgroups

	subgroup	G/H
center	C₂×C₁₃	C₂²⋊D₁₃
commutator, cosocle	C₄×C₁₃	C₂²×C₁₃
Frattini	C₄	C₂×C₁₃×D₁₃
Fitting, prime radical	D₄×C₁₃²	C₂
socle	C₂×C₁₃²	D₄
hypercenter	D₄×C₁₃	D₁₃
hypocenter	C₁₃	C₁₃×SD₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂×C₁₃ ◁ C₄×C₁₃ ◁ D₄×C₁₃

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 104

Conjugacy classes & character table

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

Relationships

maximal subgroup of	#72259250, C₁₃×#88186, #72259275, …
maximal normal subgroup of	#72259250, C₁₃×#88186, #72259275, …

GAP

Past the SmallGroups library coverage — no SmallGroups id.