C₂×C₅⋊D₅×C₁₉₇ #34089259

order	19700
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₉₇ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₅⋊D₅×C₁₉₇
unambiguous semidirect product	(C₂×C₅)⋊(D₅×C₁₉₇)

	subgroup	G/H
center, hypercenter	C₂×C₁₉₇	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₁₉₇
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₉₇	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₁₉₇

80 conjugacy classes of subgroups.

μ_t(G) = 9850

5516 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19700, 47);