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C₄×C₇×C₁₉×C₇⋊C₉ #45691519

order	33516
automorphism	?
homology	Abelianization (H₁) = C₄×C₇×C₉×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₄×C₇×C₁₉×C₇⋊C₉
unambiguous semidirect product	(C₄×C₇)⋊(C₇×C₉×C₁₉)

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₃×C₄×C₇×C₁₉	ΓL(1,𝔽₈)
commutator, hypocenter	C₇	C₄×C₇×C₉×C₁₉
Frattini	C₂×C₃	C₂×C₇×C₁₉×ΓL(1,𝔽₈)
Fitting	C₃×C₄×C₇²×C₁₉	C₃
socle, prime radical	C₂×C₃×C₇²×C₁₉	C₂×C₃
cosocle	C₂×C₃×C₇	C₂×C₃×C₇×C₁₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₃×C₄×C₇×C₁₉

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4788

Conjugacy classes & character table

7980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33516, 317);