D₅×C₂₆₈₉ #41001915

order	26890
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₆₈₉ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₅×C₂₆₈₉
unambiguous semidirect product	C₅⋊(C₂×C₂₆₈₉)

Fitting, socle, Hall	C₅×C₂₆₈₉ ⋊ C₂
derived, Sylow	C₅ ⋊ C₂×C₂₆₈₉

	subgroup	G/H
center, hypercenter	C₂₆₈₉	D₅
commutator, cosocle, hypocenter	C₅	C₂×C₂₆₈₉
Frattini	C₁	G
Fitting, socle	C₅×C₂₆₈₉	C₂
LCS	G ▷ C₅
UCS	C₁ ◁ C₂₆₈₉

8 conjugacy classes of subgroups.

μ_t(G) = 13445

10756 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26890, 1);