C₂×C₇⋊D₇×C₁₀₇ #35230491

order	20972
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₀₇ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₂×C₇⋊D₇×C₁₀₇
unambiguous semidirect product	(C₂×C₇)⋊(D₇×C₁₀₇)

	subgroup	G/H
center, hypercenter	C₂×C₁₀₇	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂²×C₁₀₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₀₇	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₁₀₇

100 conjugacy classes of subgroups.

μ_t(G) = 10486

5564 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(20972, 27);