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C₃×C₄×C₁₉×#3862 #45691951

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃×C₇

Aliases

C₃×C₄×C₁₉×#3862

Splittings

Fitting	C₃×C₄×C₇²×C₁₉ ⋊ C₃
derived, Sylow	C₇² ⋊ C₃²×C₄×C₁₉
Hall	C₄×C₇²×C₁₉ ⋊ C₃²
Hall	C₇²×C₁₉ ⋊ C₃²×C₄
Hall	C₄×C₇² ⋊ C₃²×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄×C₁₉	#3862
commutator, hypocenter	C₇²	C₃²×C₄×C₁₉
Frattini	C₂	C₂×C₃×C₁₉×#3862
Fitting	C₃×C₄×C₇²×C₁₉	C₃
socle	C₂×C₃×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₁₉×#3862	C₂
cosocle	C₂×C₇²	C₂×C₃²×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₄×C₁₉

168 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4788

Conjugacy classes & character table

4332 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 749);