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C₂×C₁₉×#64418 #26014000

order	11172
isoclinism	isoclinic class of #64418
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉ · Schur multiplier (H₂) = C₂

Aliases

C₂×C₁₉×#64418

Splittings

Fitting, socle	C₂×C₇²×C₁₉ ⋊ D₃
derived, Hall	#3862 ⋊ C₂²×C₁₉
Hall	C₁₉×#3862 ⋊ C₂²
Hall	C₇²×C₁₉ ⋊ C₂×D₃
Sylow	C₇² ⋊ C₂×D₃×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉	#64418
commutator, cosocle, hypocenter	#3862	C₂²×C₁₉
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₉	D₃
LCS	G ▷ #3862
UCS	C₁ ◁ C₂×C₁₉

68 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

760 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂×C₁₉⋊C₃×#64418, C₂×C₁₉×#64418⋊C₃, C₂×#30660727, …
maximal normal subgroup of	C₂×C₁₉⋊C₃×#64418, C₂×C₁₉×#64418⋊C₃, C₂×#30660727, …
maximal quotient of	C₂×C₁₉×#11725071, D₃×C₁₉×#64418, C₂×C₃×C₁₉×#64418, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11172, 262);