Finite Group Databasebeta

← Prev (#26013862) Next (#26013864) →

C₄×C₁₉×#3861 #26013863

order	11172
isoclinism	isoclinic class of #3861
automorphism	?
homology	Abelianization (H₁) = C₃×C₄×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₄×C₁₉×#3861

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	#3861
commutator, hypocenter	C₇²	C₃×C₄×C₁₉
Frattini	C₂	C₂×C₁₉×#3861
Fitting	C₄×C₇²×C₁₉	C₃
socle	C₂×C₇²×C₁₉	C₂×C₃
prime radical	C₂×C₁₉×#3861	C₂
cosocle	C₂×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₄×C₁₉

120 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×#3861, C₄×C₁₉×ΓL(1,𝔽₈)², C₄×#3861⋊(C₁₉⋊C₃), …
maximal normal subgroup of	C₄×C₁₉⋊C₃×#3861, C₄×C₁₉×ΓL(1,𝔽₈)², C₄×#3861⋊(C₁₉⋊C₃), …
maximal quotient of	C₄×C₁₉×#89204, Dic₃×C₁₉×#3861, C₃×C₄×C₁₉×#3861

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(11172, 125);