Finite Group Databasebeta

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C₂²×C₁₉×#66524 #38760925

order	25308
isoclinism	isoclinic class of C₃₇⋊C₃
automorphism	?
homology	Abelianization (H₁) = C₂²×C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

C₂²×C₁₉×#66524

Splittings

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

Subgroups

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

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3420 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25308, 69);