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C₁₉×Dic₉×C₄₇ #44565246

order	32148
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×Dic₉×C₄₇
unambiguous semidirect product	C₉⋊(C₄×C₁₉×C₄₇)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₄₇	D₉
commutator, hypocenter	C₉	C₄×C₁₉×C₄₇
Frattini	C₂×C₃	D₃×C₁₉×C₄₇
Fitting	C₂×C₉×C₁₉×C₄₇	C₂
socle, prime radical	C₂×C₃×C₁₉×C₄₇	D₃
cosocle	C₂×C₉	C₂×C₁₉×C₄₇
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₉×C₄₇

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 32148

Conjugacy classes & character table

10716 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32148, 6);