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C₄×C₁₉×C₁₁²⋊C₃ #42119958

order	27588
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁₁

Aliases

direct product	C₄×C₁₉×C₁₁²⋊C₃
unambiguous semidirect product	(C₄×C₁₁²)⋊(C₃×C₁₉)

Splittings

Fitting, Hall	C₄×C₁₁²×C₁₉ ⋊ C₃
derived, Sylow	C₁₁² ⋊ C₃×C₄×C₁₉
Hall	C₁₁²×C₁₉ ⋊ C₃×C₄
Hall	C₄×C₁₁² ⋊ C₃×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₁₉	C₁₁²⋊C₃
commutator, hypocenter	C₁₁²	C₃×C₄×C₁₉
Frattini	C₂	C₂×C₁₉×C₁₁²⋊C₃
Fitting	C₄×C₁₁²×C₁₉	C₃
socle	C₂×C₁₁²×C₁₉	C₂×C₃
prime radical	C₂×C₁₉×C₁₁²⋊C₃	C₂
cosocle	C₂×C₁₁²	C₂×C₃×C₁₉
LCS	G ▷ C₁₁²
UCS	C₁ ◁ C₄×C₁₉

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 2508

Conjugacy classes & character table

3268 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27588, 50);