C₂×C₇⋊D₇×C₁₃₇ #41001667

order	26852
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₃₇ · Schur multiplier (H₂) = C₂×C₇

Aliases

direct product	C₂×C₇⋊D₇×C₁₃₇
unambiguous semidirect product	(C₂×C₇)⋊(D₇×C₁₃₇)

	subgroup	G/H
center, hypercenter	C₂×C₁₃₇	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂²×C₁₃₇
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₃₇	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₂×C₁₃₇

100 conjugacy classes of subgroups.

μ_t(G) = 13426

7124 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26852, 33);