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C₃×C₁₉×C₃⋊(C₇⋊Dic₇) #45691966

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

Aliases

direct product	C₃×C₁₉×C₃⋊(C₇⋊Dic₇)
unambiguous semidirect product	C₃⋊(C₃×C₁₉×C₇⋊Dic₇)

Splittings

derived	C₃×C₇² ⋊ C₃×C₄×C₁₉
Hall	C₃²×C₇²×C₁₉ ⋊ C₄
Hall	C₇²×C₁₉ ⋊ C₃×Dic₃
Hall	C₃²×C₇² ⋊ C₄×C₁₉
Hall	C₃²×C₁₉ ⋊ C₇⋊Dic₇
Sylow	C₇² ⋊ C₃×Dic₃×C₁₉
Sylow	C₃² ⋊ C₁₉×C₇⋊Dic₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	C₃⋊(C₇⋊D₇)
commutator, hypocenter	C₃×C₇²	C₃×C₄×C₁₉
Frattini	C₂	C₃×C₁₉×C₃⋊(C₇⋊D₇)
Fitting, socle, prime radical	C₂×C₃²×C₇²×C₁₉	C₂
cosocle	C₂×C₃×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₃×C₇²
UCS	C₁ ◁ C₂×C₃×C₁₉

280 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 11172

Conjugacy classes & character table

8550 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 764);