C₅²⋊C₃×C₃₁₃ #37553403

order	23475
automorphism	?
homology	Abelianization (H₁) = C₃×C₃₁₃ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅²⋊C₃×C₃₁₃
unambiguous semidirect product	C₅²⋊(C₃×C₃₁₃)

Fitting, socle, Hall	C₅²×C₃₁₃ ⋊ C₃
derived, Sylow	C₅² ⋊ C₃×C₃₁₃

	subgroup	G/H
center, hypercenter	C₃₁₃	C₅²⋊C₃
commutator, cosocle, hypocenter	C₅²	C₃×C₃₁₃
Frattini	C₁	G
Fitting, socle	C₅²×C₃₁₃	C₃
LCS	G ▷ C₅²
UCS	C₁ ◁ C₃₁₃

12 conjugacy classes of subgroups.

μ_t(G) = 4695

3443 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23475, 4);