C₇⋊D₇×C₃₅₃ #46829237

order	34594
automorphism	?
homology	Abelianization (H₁) = C₂×C₃₅₃ · Schur multiplier (H₂) = C₇

Aliases

direct product	C₇⋊D₇×C₃₅₃
unambiguous semidirect product	C₇⋊(D₇×C₃₅₃)

Fitting, socle, Hall	C₇²×C₃₅₃ ⋊ C₂
derived, Sylow	C₇² ⋊ C₂×C₃₅₃

	subgroup	G/H
center, hypercenter	C₃₅₃	C₇⋊D₇
commutator, cosocle, hypocenter	C₇²	C₂×C₃₅₃
Frattini	C₁	G
Fitting, socle	C₇²×C₃₅₃	C₂
LCS	G ▷ C₇²
UCS	C₁ ◁ C₃₅₃

40 conjugacy classes of subgroups.

μ_t(G) = 17297

9178 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34594, 9);