Finite Group Databasebeta

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C₄×C₄₇×#4294 #44565242

order	32148
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

C₄×C₄₇×#4294

Splittings

derived, Sylow	C₁₉ ⋊ C₄×C₉×C₄₇
Hall	C₄×C₁₉×C₄₇ ⋊ C₉
Hall	C₁₉×C₄₇ ⋊ C₄×C₉
Hall	C₄×C₁₉ ⋊ C₉×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄×C₄₇	C₁₉⋊C₃
commutator, hypocenter	C₁₉	C₄×C₉×C₄₇
Frattini	C₂×C₃	C₂×C₄₇×C₁₉⋊C₃
Fitting	C₃×C₄×C₁₉×C₄₇	C₃
socle, prime radical	C₂×C₃×C₁₉×C₄₇	C₂×C₃
cosocle	C₂×C₃×C₁₉	C₂×C₃×C₄₇
LCS	G ▷ C₁₉
UCS	C₁ ◁ C₃×C₄×C₄₇

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 32148

Conjugacy classes & character table

5076 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 2);