Finite Group Databasebeta

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C₂×C₃₇×D₁₇₁ #38760927

order	25308
isoclinism	isoclinic class of D₁₇₁
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₃₇×D₁₇₁
unambiguous semidirect product	(C₂×C₉)⋊(C₃₇×D₁₉)
unambiguous semidirect product	(C₂×C₁₉)⋊(D₉×C₃₇)

Splittings

Fitting	C₂×C₉×C₁₉×C₃₇ ⋊ C₂
derived, Hall	C₉×C₁₉ ⋊ C₂²×C₃₇
Hall	C₉×C₁₉×C₃₇ ⋊ C₂²
Hall	C₁₉×C₃₇ ⋊ C₂×D₉
Hall	C₉×C₃₇ ⋊ C₂×D₁₉
Sylow	C₁₉ ⋊ C₂×D₉×C₃₇
Sylow	C₉ ⋊ C₂×C₃₇×D₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃₇	D₁₇₁
commutator, hypocenter	C₉×C₁₉	C₂²×C₃₇
Frattini	C₃	C₂×C₃₇×D₅₇
Fitting	C₂×C₉×C₁₉×C₃₇	C₂
socle	C₂×C₃×C₁₉×C₃₇	D₃
LCS	G ▷ C₉×C₁₉
UCS	C₁ ◁ C₂×C₃₇

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6438 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25308, 71);