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Dic₃×C₁₉×C₁₆₇ #49185148

order	38076
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₁₆₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	Dic₃×C₁₉×C₁₆₇
unambiguous semidirect product	C₃⋊(C₄×C₁₉×C₁₆₇)

Splittings

derived, Sylow	C₃ ⋊ C₄×C₁₉×C₁₆₇
Hall	C₃×C₁₉×C₁₆₇ ⋊ C₄
Hall	C₃×C₁₆₇ ⋊ C₄×C₁₉
Hall	C₃×C₁₉ ⋊ C₄×C₁₆₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₁₆₇	D₃
commutator, hypocenter	C₃	C₄×C₁₉×C₁₆₇
Frattini	C₂	D₃×C₁₉×C₁₆₇
Fitting, socle, prime radical	C₂×C₃×C₁₉×C₁₆₇	C₂
cosocle	C₂×C₃	C₂×C₁₉×C₁₆₇
LCS	G ▷ C₃
UCS	C₁ ◁ C₂×C₁₉×C₁₆₇

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 38076

Conjugacy classes & character table

19038 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38076, 6);