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C₂×C₄×D₃×C₁₉ #11744973

order	912
isoclinism	isoclinic class of D₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₉ · Schur multiplier (H₂) = C₂³

Aliases

C₂×C₄×D₃×C₁₉

Splittings

Fitting	C₂×C₃×C₄×C₁₉ ⋊ C₂
derived, Sylow	C₃ ⋊ C₂²×C₄×C₁₉
Hall	C₃×C₁₉ ⋊ C₂²×C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₄×C₁₉	D₃
commutator, hypocenter	C₃	C₂²×C₄×C₁₉
Frattini	C₂	C₂²×D₃×C₁₉
Fitting	C₂×C₃×C₄×C₁₉	C₂
socle	C₂²×C₃×C₁₉	C₂²
prime radical	C₂²×D₃×C₁₉	C₂
cosocle	C₂×C₃	C₂³×C₁₉
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₁₉

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 456

Conjugacy classes & character table

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

Relationships

maximal subgroup of	(C₂×D₃)⋊(C₁₉⋊C₈), C₁₉×(C₂×D₃)⋊C₈, #14269205, …
maximal normal subgroup of	(C₂×D₃)⋊(C₁₉⋊C₈), C₁₉×(C₂×D₃)⋊C₈, #14269205, …
maximal quotient of	C₄×C₁₉×Dic₆, C₄²×D₃×C₁₉, C₁₉×#872, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 184);