Finite Group Databasebeta

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C₂×C₁₉×D₃₃₃ #38760928

order	25308
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₁₉×D₃₃₃
unambiguous semidirect product	(C₂×C₉)⋊(C₁₉×D₃₇)
unambiguous semidirect product	(C₂×C₃₇)⋊(D₉×C₁₉)

Splittings

Fitting	C₂×C₉×C₁₉×C₃₇ ⋊ C₂
derived, Hall	C₉×C₃₇ ⋊ C₂²×C₁₉
Hall	C₉×C₁₉×C₃₇ ⋊ C₂²
Hall	C₁₉×C₃₇ ⋊ C₂×D₉
Hall	C₉×C₁₉ ⋊ C₂×D₃₇
Sylow	C₃₇ ⋊ C₂×D₉×C₁₉
Sylow	C₉ ⋊ C₂×C₁₉×D₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₃₃₃
commutator, hypocenter	C₉×C₃₇	C₂²×C₁₉
Frattini	C₃	C₂×C₁₉×D₁₁₁
Fitting	C₂×C₉×C₁₉×C₃₇	C₂
socle	C₂×C₃×C₁₉×C₃₇	D₃
LCS	G ▷ C₉×C₃₇
UCS	C₁ ◁ C₂×C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

6384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25308, 72);