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C₄₇×C₂²⋊#4294 #44565265

order	32148
automorphism	?
homology	Abelianization (H₁) = C₉×C₄₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₄₇×C₂²⋊#4294
unambiguous semidirect product	C₂²⋊(C₄₇×#4294)
unambiguous semidirect product	(C₂²×C₄₇)⋊#4294

Splittings

derived, Hall	C₂²×C₁₉ ⋊ C₉×C₄₇
Hall	C₂²×C₁₉×C₄₇ ⋊ C₉
Hall	C₁₉×C₄₇ ⋊ C₂²⋊C₉
Hall	C₂²×C₄₇ ⋊ #4294
Sylow	C₁₉ ⋊ C₂²⋊C₉×C₄₇
Sylow	C₂² ⋊ C₄₇×#4294

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄₇	C₂²⋊(C₁₉⋊C₃)
commutator, hypocenter	C₂²×C₁₉	C₉×C₄₇
Frattini	C₃	C₄₇×C₂²⋊(C₁₉⋊C₃)
Fitting, socle, prime radical	C₂²×C₃×C₁₉×C₄₇	C₃
cosocle	C₂²×C₃×C₁₉	C₃×C₄₇
LCS	G ▷ C₂²×C₁₉
UCS	C₁ ◁ C₃×C₄₇

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 16074

Conjugacy classes & character table

3948 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 25);