C₅⋊D₅×C₅₆₉ #43249588

order	28450
automorphism	?
homology	Abelianization (H₁) = C₂×C₅₆₉ · Schur multiplier (H₂) = C₅

Aliases

direct product	C₅⋊D₅×C₅₆₉
unambiguous semidirect product	C₅⋊(D₅×C₅₆₉)

Fitting, socle, Hall	C₅²×C₅₆₉ ⋊ C₂
derived, Sylow	C₅² ⋊ C₂×C₅₆₉

	subgroup	G/H
center, hypercenter	C₅₆₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂×C₅₆₉
Frattini	C₁	G
Fitting, socle	C₅²×C₅₆₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₅₆₉

32 conjugacy classes of subgroups.

μ_t(G) = 14225

7966 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(28450, 9);