C₂×C₅⋊D₅×C₂₆₉ #41001993

order	26900
automorphism	?
homology	Abelianization (H₁) = C₂²×C₂₆₉ · Schur multiplier (H₂) = C₂×C₅

Aliases

direct product	C₂×C₅⋊D₅×C₂₆₉
unambiguous semidirect product	(C₂×C₅)⋊(D₅×C₂₆₉)

	subgroup	G/H
center, hypercenter	C₂×C₂₆₉	C₅⋊D₅
commutator, cosocle, hypocenter	C₅²	C₂²×C₂₆₉
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₂₆₉	C₂
LCS	G ▷ C₅²
UCS	C₁ ◁ C₂×C₂₆₉

80 conjugacy classes of subgroups.

μ_t(G) = 13450

7532 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26900, 49);