C₂×C₅×D₁₆₁₅ #44568125

order	32300
automorphism	?
homology	Abelianization (H₁) = C₂²×C₅ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₂×C₅×D₁₆₁₅
unambiguous semidirect product	(C₂×C₅)⋊(C₅×D₃₂₃)
unambiguous semidirect product	(C₂×C₁₇)⋊(C₅×D₉₅)
unambiguous semidirect product	(C₂×C₁₉)⋊(C₅×D₈₅)

	subgroup	G/H
center, hypercenter	C₂×C₅	D₁₆₁₅
commutator, cosocle, hypocenter	C₅×C₁₇×C₁₉	C₂²×C₅
Frattini	C₁	G
Fitting, socle	C₂×C₅²×C₁₇×C₁₉	C₂
LCS	G ▷ C₅×C₁₇×C₁₉
UCS	C₁ ◁ C₂×C₅

96 conjugacy classes of subgroups.

μ_t(G) = 6460

8090 conjugacy classes. The character table is too large to display.

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32300, 114);