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C₄×C₁₉×#3862 #26013866

order	11172
isoclinism	isoclinic class of #3862
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₇

Aliases

C₄×C₁₉×#3862

Splittings

Fitting, Hall	C₄×C₇²×C₁₉ ⋊ C₃
derived, Sylow	C₇² ⋊ C₃×C₄×C₁₉
Hall	C₇²×C₁₉ ⋊ C₃×C₄
Hall	C₄×C₇² ⋊ C₃×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₁₉	#3862
commutator, hypocenter	C₇²	C₃×C₄×C₁₉
Frattini	C₂	C₂×C₁₉×#3862
Fitting	C₄×C₇²×C₁₉	C₃
socle	C₂×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₁₉×#3862	C₂
cosocle	C₂×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₄×C₁₉

60 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1444 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₄×C₁₉⋊C₃×#3862, C₄×C₁₉×ΓL(1,𝔽₈)², C₄×#22552727, …
maximal normal subgroup of	C₄×C₁₉⋊C₃×#3862, C₄×C₁₉×ΓL(1,𝔽₈)², C₄×#22552727, …
maximal quotient of	C₄×C₁₉×#89205, Dic₃×C₁₉×#3862, C₃×C₄×C₁₉×#3862

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11172, 128);