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C₅×C₁₉×Dic₈₉ #46799031

order	33820
automorphism	?
homology	Abelianization (H₁) = C₄×C₅×C₁₉ · Schur multiplier (H₂) = C₁

Aliases

C₅×C₁₉×Dic₈₉

Splittings

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

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₅×C₁₉	D₈₉
commutator, hypocenter	C₈₉	C₄×C₅×C₁₉
Frattini	C₂	C₅×C₁₉×D₈₉
Fitting, socle, prime radical	C₂×C₅×C₁₉×C₈₉	C₂
cosocle	C₂×C₈₉	C₂×C₅×C₁₉
LCS	G ▷ C₈₉
UCS	C₁ ◁ C₂×C₅×C₁₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 33820

Conjugacy classes & character table

8740 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33820, 2);