Finite Group Databasebeta

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C₁₉×Dic₇×C₇⋊C₉ #45691508

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₉×Dic₇×C₇⋊C₉

Splittings

derived, Sylow	C₇² ⋊ C₄×C₉×C₁₉
Hall	C₇×C₁₉×C₇⋊C₉ ⋊ C₄
Hall	C₇×C₁₉×Dic₇ ⋊ C₉
Hall	C₇²×C₁₉ ⋊ C₄×C₉
Hall	C₇×C₇⋊C₉ ⋊ C₄×C₁₉
Hall	C₇×Dic₇ ⋊ C₉×C₁₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃×C₁₉	D₇×ΓL(1,𝔽₈)
commutator, hypocenter	C₇²	C₄×C₉×C₁₉
Frattini	C₂×C₃	D₇×C₁₉×ΓL(1,𝔽₈)
Fitting, socle, prime radical	C₂×C₃×C₇²×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₇²	C₂×C₃×C₁₉
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₃×C₁₉

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4788

Conjugacy classes & character table

2850 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 306);