Finite Group Databasebeta

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C₁₉×C₂²⋊#66524 #38760920

order	25308
automorphism	?
homology	Abelianization (H₁) = C₉×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₁₉×C₂²⋊#66524
unambiguous semidirect product	C₂²⋊(C₁₉×#66524)

Splittings

derived, Hall	C₂²×C₃₇ ⋊ C₉×C₁₉
Hall	C₂²×C₁₉×C₃₇ ⋊ C₉
Hall	C₁₉×C₃₇ ⋊ C₂²⋊C₉
Hall	C₂²×C₁₉ ⋊ #66524
Sylow	C₃₇ ⋊ C₁₉×C₂²⋊C₉
Sylow	C₂² ⋊ C₁₉×#66524

Subgroups

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

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2964 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25308, 64);