Finite Group Databasebeta

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C₁₉×C₉⋊#3866 #38760909

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

Aliases

direct product	C₁₉×C₉⋊#3866
unambiguous semidirect product	C₉⋊(C₁₉×#3866)

Splittings

Fitting, Hall	C₉×C₁₉×C₃₇ ⋊ C₄
derived, Hall	C₉×C₃₇ ⋊ C₄×C₁₉
Hall	C₁₉×C₃₇ ⋊ Dic₉
Hall	C₉×C₁₉ ⋊ #3866
Sylow	C₃₇ ⋊ C₁₉×Dic₉
Sylow	C₉ ⋊ C₁₉×#3866

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉	C₉⋊#3866
commutator, hypocenter	C₉×C₃₇	C₄×C₁₉
Frattini	C₃	C₁₉×C₃⋊#3866
Fitting	C₉×C₁₉×C₃₇	C₄
socle	C₃×C₁₉×C₃₇	Dic₃
LCS	G ▷ C₉×C₃₇
UCS	C₁ ◁ C₁₉

36 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1767 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25308, 53);