Finite Group Databasebeta

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C₃²×C₁₉×C₇⋊Dic₇ #45691972

order	33516
automorphism	?
homology	Abelianization (H₁) = C₃²×C₄×C₁₉ · Schur multiplier (H₂) = C₃×C₇

Aliases

C₃²×C₁₉×C₇⋊Dic₇

Splittings

derived, Sylow	C₇² ⋊ C₃²×C₄×C₁₉
Hall	C₃²×C₇²×C₁₉ ⋊ C₄
Hall	C₇²×C₁₉ ⋊ C₃²×C₄
Hall	C₃²×C₇² ⋊ C₄×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃²×C₁₉	C₇⋊D₇
commutator, hypocenter	C₇²	C₃²×C₄×C₁₉
Frattini	C₂	C₃²×C₁₉×C₇⋊D₇
Fitting, socle, prime radical	C₂×C₃²×C₇²×C₁₉	C₂
cosocle	C₂×C₇²	C₂×C₃²×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃²×C₁₉

360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 33516

Conjugacy classes & character table

8892 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 770);