Finite Group Databasebeta

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C₁₉×Dic₅×C₇₉ #44473173

order	30020
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₇₉ · Schur multiplier (H₂) = C₁

Aliases

C₁₉×Dic₅×C₇₉

Splittings

derived, Sylow	C₅ ⋊ C₄×C₁₉×C₇₉
Hall	C₅×C₁₉×C₇₉ ⋊ C₄
Hall	C₅×C₇₉ ⋊ C₄×C₁₉
Hall	C₅×C₁₉ ⋊ C₄×C₇₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₇₉	D₅
commutator, hypocenter	C₅	C₄×C₁₉×C₇₉
Frattini	C₂	D₅×C₁₉×C₇₉
Fitting, socle, prime radical	C₂×C₅×C₁₉×C₇₉	C₂
cosocle	C₂×C₅	C₂×C₁₉×C₇₉
LCS	G ▷ C₅
UCS	C₁ ◁ C₂×C₁₉×C₇₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 30020

Conjugacy classes & character table

12008 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30020, 5);