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C₃²×C₁₉×Dic₄₇ #44565298

order	32148
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

direct product	C₃²×C₁₉×Dic₄₇
unambiguous semidirect product	C₄₇⋊(C₃²×C₄×C₁₉)

Splittings

derived, Sylow	C₄₇ ⋊ C₃²×C₄×C₁₉
Hall	C₃²×C₁₉×C₄₇ ⋊ C₄
Hall	C₁₉×C₄₇ ⋊ C₃²×C₄
Hall	C₃²×C₄₇ ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₉	D₄₇
commutator, hypocenter	C₄₇	C₃²×C₄×C₁₉
Frattini	C₂	C₃²×C₁₉×D₄₇
Fitting, socle, prime radical	C₂×C₃²×C₁₉×C₄₇	C₂
cosocle	C₂×C₄₇	C₂×C₃²×C₁₉
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂×C₃²×C₁₉

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 32148

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(32148, 58);