C₃×C₅⋊((C₂²⋊C₉)⋊C₂) #11761947

order	1080
isoclinism	isoclinic class of C₅⋊((C₂²⋊C₉)⋊C₂)
automorphism	?
homology	Abelianization (H₁) = C₂×C₃ · Schur multiplier (H₂) = C₂

Aliases

direct product	C₃×C₅⋊((C₂²⋊C₉)⋊C₂)
unambiguous semidirect product	C₅⋊(C₃×(C₂²⋊C₉)⋊C₂)

derived	C₅×C₂²⋊C₉ ⋊ C₂×C₃
Sylow	C₅ ⋊ C₃×(C₂²⋊C₉)⋊C₂

	subgroup	G/H
center, hypercenter	C₃	C₅⋊((C₂²⋊C₉)⋊C₂)
commutator, cosocle, hypocenter	C₅×C₂²⋊C₉	C₂×C₃
Frattini	C₃	C₃×C₅⋊S₄
Fitting, socle	C₂²×C₃²×C₅	D₃
LCS	G ▷ C₅×C₂²⋊C₉
UCS	C₁ ◁ C₃

82 conjugacy classes of subgroups.

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 180

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1080, 293);