C₅₃×D₂₅₁ #40998323

order	26606
automorphism	?
homology	Abelianization (H₁) = C₂×C₅₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₅₃×D₂₅₁
unambiguous semidirect product	C₂₅₁⋊(C₂×C₅₃)

Fitting, socle, Hall	C₅₃×C₂₅₁ ⋊ C₂
derived, Sylow	C₂₅₁ ⋊ C₂×C₅₃

	subgroup	G/H
center, hypercenter	C₅₃	D₂₅₁
commutator, cosocle, hypocenter	C₂₅₁	C₂×C₅₃
Frattini	C₁	G
Fitting, socle	C₅₃×C₂₅₁	C₂
LCS	G ▷ C₂₅₁
UCS	C₁ ◁ C₅₃

8 conjugacy classes of subgroups.

μ_t(G) = 13303

6731 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26606, 2);