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C₁₉×AGL(1,𝔽₅)×C₈₉ #46799042

order	33820
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₈₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₉×AGL(1,𝔽₅)×C₈₉

Splittings

Fitting, socle, Hall	C₅×C₁₉×C₈₉ ⋊ C₄
derived, Sylow	C₅ ⋊ C₄×C₁₉×C₈₉
Hall	C₅×C₈₉ ⋊ C₄×C₁₉
Hall	C₅×C₁₉ ⋊ C₄×C₈₉

Subgroups

	subgroup	G/H
center, hypercenter	C₁₉×C₈₉	AGL(1,𝔽₅)
commutator, hypocenter	C₅	C₄×C₁₉×C₈₉
Frattini	C₁	G
Fitting, socle	C₅×C₁₉×C₈₉	C₄
prime radical	D₅×C₁₉×C₈₉	C₂
cosocle	D₅	C₂×C₁₉×C₈₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₁₉×C₈₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 8455

Conjugacy classes & character table

8455 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33820, 13);