Finite Group Databasebeta

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C₄×C₇×#11924780 #45691817

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₇×C₉ · Schur multiplier (H₂) = C₁

Aliases

C₄×C₇×#11924780

Splittings

Fitting, Hall	C₄×C₇²×C₁₉ ⋊ C₉
derived	C₇×C₁₉ ⋊ C₄×C₇×C₉
Hall	C₇²×C₁₉ ⋊ C₄×C₉
Hall	C₄×C₇² ⋊ #4296
Hall	C₄×C₁₉ ⋊ C₇×C₇⋊C₉
Sylow	C₇² ⋊ C₄×#4296
Sylow	C₁₉ ⋊ C₄×C₇×C₇⋊C₉

Subgroups

	subgroup	G/H
center, hypercenter	C₄×C₇	#11924780
commutator, hypocenter	C₇×C₁₉	C₄×C₇×C₉
Frattini	C₂	C₂×C₇×#11924780
Fitting	C₄×C₇²×C₁₉	C₉
socle	C₂×C₇²×C₁₉	C₂×C₉
prime radical	C₂×C₇²×C₁₉⋊C₃	C₂×C₃
cosocle	C₂×C₇×C₁₉⋊C₃	C₂×C₃×C₇
LCS	G ▷ C₇×C₁₉
UCS	C₁ ◁ C₄×C₇

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 1596

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 615);