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C₃×C₁₉×#3861 #22552736

order	8379
isoclinism	isoclinic class of #3861
automorphism	?
homology	Abelianization (H₁) = C₃²×C₁₉ · Schur multiplier (H₂) = C₃

Aliases

C₃×C₁₉×#3861

Splittings

Fitting, socle	C₃×C₇²×C₁₉ ⋊ C₃
derived, Sylow	C₇² ⋊ C₃²×C₁₉
Hall	C₇²×C₁₉ ⋊ C₃²

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₁₉	#3861
commutator, hypocenter	C₇²	C₃²×C₁₉
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₉	C₃
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃×C₁₉

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1083 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₃×C₁₉×#64424, C₃×#19150288, C₃×C₁₉×#64423, …
maximal normal subgroup of	C₃×C₁₉×#64424, C₃×#19150288, C₃×C₁₉×#64423, …
maximal quotient of	C₂×C₃×C₁₉×#3861, A₄×C₁₉×#3861, C₃×C₁₉×C₂²⋊#3861

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8379, 48);