C₇×C₂²⋊(C₁₉₃⋊C₃) #30633901

order	16212
automorphism	?
homology	Abelianization (H₁) = C₃×C₇ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₇×C₂²⋊(C₁₉₃⋊C₃)
unambiguous semidirect product	C₂²⋊(C₇×C₁₉₃⋊C₃)
unambiguous semidirect product	C₁₉₃⋊(C₇×A₄)

	subgroup	G/H
center, hypercenter	C₇	C₂²⋊(C₁₉₃⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₁₉₃	C₃×C₇
Frattini	C₁	G
Fitting, socle	C₂²×C₇×C₁₉₃	C₃
LCS	G ▷ C₂²×C₁₉₃
UCS	C₁ ◁ C₇

20 conjugacy classes of subgroups.

μ_t(G) = 5404

1820 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16212, 64);