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C₄²×C₁₉⋊C₃ #11744837

order	912
isoclinism	isoclinic class of C₁₉⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄² · Schur multiplier (H₂) = C₄

Aliases

C₄²×C₁₉⋊C₃

Splittings

Fitting, Hall	C₄²×C₁₉ ⋊ C₃
derived, Sylow	C₁₉ ⋊ C₃×C₄²

Subgroups

	subgroup	G/H
center, hypercenter	C₄²	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₃×C₄²
Frattini	C₂²	C₂²×C₁₉⋊C₃
Fitting	C₄²×C₁₉	C₃
socle, cosocle	C₂²×C₁₉	C₂²×C₃
prime radical	C₂²×C₁₉⋊C₃	C₂²
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₄²

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 304

Conjugacy classes & character table

144 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₄×(C₁₉⋊C₃)⋊C₈, #10597260⋊C₃, C₄⋊((C₁₉⋊C₃)⋊C₈), …
maximal normal subgroup of	C₄×(C₁₉⋊C₃)⋊C₈, #10597260⋊C₃, C₄⋊((C₁₉⋊C₃)⋊C₈), …
maximal quotient of	#95×C₁₉⋊C₃, C₄×C₈×C₁₉⋊C₃, #97×C₁₉⋊C₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(912, 48);