C₂₃×D₄₅ #14523392

order	2070
isoclinism	isoclinic class of D₄₅
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×D₄₅
unambiguous semidirect product	C₅⋊(D₉×C₂₃)
unambiguous semidirect product	C₉⋊(D₅×C₂₃)

	subgroup	G/H
center, hypercenter	C₂₃	D₄₅
commutator, cosocle, hypocenter	C₅×C₉	C₂×C₂₃
Frattini	C₃	C₂₃×D₁₅
Fitting	C₅×C₉×C₂₃	C₂
socle	C₃×C₅×C₂₃	D₃
LCS	G ▷ C₅×C₉
UCS	C₁ ◁ C₂₃

24 conjugacy classes of subgroups.

minimal degree	μ(G) = 37
transitive degree	μ_t(G) = 1035

A minimal faithful permutation representation — 2 generators on 37 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32)(33,34,35,36,37);(25,32)(26,31)(27,30)(28,29)(34,37)(35,36)

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2070, 7);