C₇×C₁₃×C₂²⋊(C₅²⋊C₃) #41032073

order	27300
automorphism	?
homology	Abelianization (H₁) = C₃×C₇×C₁₃ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₇×C₁₃×C₂²⋊(C₅²⋊C₃)
unambiguous semidirect product	C₂²⋊(C₇×C₁₃×C₅²⋊C₃)
unambiguous semidirect product	C₅²⋊(C₇×A₄×C₁₃)

	subgroup	G/H
center, hypercenter	C₇×C₁₃	C₂²⋊(C₅²⋊C₃)
commutator, cosocle, hypocenter	C₂²×C₅²	C₃×C₇×C₁₃
Frattini	C₁	G
Fitting, socle	C₂²×C₅²×C₇×C₁₃	C₃
LCS	G ▷ C₂²×C₅²
UCS	C₁ ◁ C₇×C₁₃

80 conjugacy classes of subgroups.

μ_t(G) = 2730

3276 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 963);