Finite Group Databasebeta

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C₁₉×Dic₉×C₃₇ #38760865

order	25308
isoclinism	isoclinic class of D₉
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₃₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×Dic₉×C₃₇
unambiguous semidirect product	C₉⋊(C₄×C₁₉×C₃₇)

Splittings

derived, Sylow	C₉ ⋊ C₄×C₁₉×C₃₇
Hall	C₉×C₁₉×C₃₇ ⋊ C₄
Hall	C₉×C₃₇ ⋊ C₄×C₁₉
Hall	C₉×C₁₉ ⋊ C₄×C₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₃₇	D₉
commutator, hypocenter	C₉	C₄×C₁₉×C₃₇
Frattini	C₂×C₃	D₃×C₁₉×C₃₇
Fitting	C₂×C₉×C₁₉×C₃₇	C₂
socle	C₂×C₃×C₁₉×C₃₇	D₃
LCS	G ▷ C₉
UCS	C₁ ◁ C₂×C₁₉×C₃₇

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

8436 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25308, 9);