Finite Group Databasebeta

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C₁₉×Dic₇×C₅₉ #44535996

order	31388
automorphism	?
homology	Abelianization (H₁) = C₄×C₁₉×C₅₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₁₉×Dic₇×C₅₉
unambiguous semidirect product	C₇⋊(C₄×C₁₉×C₅₉)

Splittings

derived, Sylow	C₇ ⋊ C₄×C₁₉×C₅₉
Hall	C₇×C₁₉×C₅₉ ⋊ C₄
Hall	C₇×C₅₉ ⋊ C₄×C₁₉
Hall	C₇×C₁₉ ⋊ C₄×C₅₉

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₁₉×C₅₉	D₇
commutator, hypocenter	C₇	C₄×C₁₉×C₅₉
Frattini	C₂	D₇×C₁₉×C₅₉
Fitting, socle, prime radical	C₂×C₇×C₁₉×C₅₉	C₂
cosocle	C₂×C₇	C₂×C₁₉×C₅₉
LCS	G ▷ C₇
UCS	C₁ ◁ C₂×C₁₉×C₅₉

24 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 31388

Conjugacy classes & character table

11210 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31388, 5);