Finite Group Databasebeta

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C₂×C₉×C₁₉×D₃₇ #38760932

order	25308
isoclinism	isoclinic class of D₃₇
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₉×C₁₉×D₃₇

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₉×C₁₉	D₃₇
commutator, hypocenter	C₃₇	C₂²×C₉×C₁₉
Frattini	C₃	C₂×C₃×C₁₉×D₃₇
Fitting	C₂×C₉×C₁₉×C₃₇	C₂
socle	C₂×C₃×C₁₉×C₃₇	C₂×C₃
LCS	G ▷ C₃₇
UCS	C₁ ◁ C₂×C₉×C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6840 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25308, 76);