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C₄⋊C₈×C₁₉⋊C₈ #18073662

order	4864
automorphism	?
homology	Abelianization (H₁) = C₂×C₈² · Schur multiplier (H₂) = C₂²×C₈

Aliases

C₄⋊C₈×C₁₉⋊C₈

Splittings

C₁₉ ⋊ C₈×C₄⋊C₈

Subgroups

	subgroup	G/H
center, Frattini	C₂×C₄²	C₂²×D₁₉
commutator	C₂×C₁₉	C₂×C₈²
Fitting	C₄×C₁₉×C₄⋊C₈	C₂
socle, prime radical	C₂³×C₁₉	C₂×C₄²
cosocle	C₂×C₄²×C₁₉	C₂³
hypercenter	C₄×C₄⋊C₈	D₁₉
hypocenter	C₁₉	C₈×C₄⋊C₈
LCS	G ▷ C₂×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₂×C₄² ◁ C₄×C₄⋊C₈

550 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degree

μ_t(G) = 4864

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4864, 60691);