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C₃×Dic₇×C₁₉⋊C₃ #18012177

order	4788
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄ · Schur multiplier (H₂) = C₃

Aliases

C₃×Dic₇×C₁₉⋊C₃

Splittings

derived, Hall	C₇×C₁₉ ⋊ C₃²×C₄
Hall	C₃×C₇×C₁₉⋊C₃ ⋊ C₄
Hall	C₁₉×Dic₇ ⋊ C₃²
Sylow	C₁₉ ⋊ C₃²×Dic₇
Sylow	C₇ ⋊ C₃×C₄×C₁₉⋊C₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₇×C₁₉⋊C₃
commutator, hypocenter	C₇×C₁₉	C₃²×C₄
Frattini	C₂	C₃×D₇×C₁₉⋊C₃
Fitting, socle	C₂×C₃×C₇×C₁₉	C₂×C₃
prime radical	C₂×C₃×C₇×C₁₉⋊C₃	C₂
cosocle	C₂×C₇×C₁₉	C₂×C₃²
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₂×C₃

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1596

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₃×C₅×Dic₇×C₁₉⋊C₃, C₃×C₁₉⋊C₃×Dic₃₅, C₃×C₁₉⋊C₃×C₇⋊AGL(1,𝔽₅), …
maximal normal subgroup of	C₃×C₅×Dic₇×C₁₉⋊C₃, C₃×C₇×Dic₇×C₁₉⋊C₃
maximal quotient of	C₃×C₅×Dic₇×C₁₉⋊C₃, C₃×C₁₉⋊C₃×Dic₃₅, C₃×C₁₉⋊C₃×C₇⋊AGL(1,𝔽₅), …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4788, 93);