Finite Group Databasebeta

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C₁₉×Dic₃₃₃ #38760866

order	25308
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×Dic₃₃₃
unambiguous semidirect product	C₉⋊(C₁₉×Dic₃₇)

Splittings

derived, Hall	C₉×C₃₇ ⋊ C₄×C₁₉
Hall	C₉×C₁₉×C₃₇ ⋊ C₄
Hall	C₁₉×C₃₇ ⋊ Dic₉
Hall	C₉×C₁₉ ⋊ Dic₃₇
Sylow	C₃₇ ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₁₉×Dic₃₇

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	D₃₃₃
commutator, hypocenter	C₉×C₃₇	C₄×C₁₉
Frattini	C₂×C₃	C₁₉×D₁₁₁
Fitting	C₂×C₉×C₁₉×C₃₇	C₂
socle	C₂×C₃×C₁₉×C₃₇	D₃
LCS	G ▷ C₉×C₃₇
UCS	C₁ ◁ C₂×C₁₉

36 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, 10);