C₂₃×D₄₃ #14520372

order	1978
isoclinism	isoclinic class of D₄₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₂₃ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₂₃×D₄₃
unambiguous semidirect product	C₄₃⋊(C₂×C₂₃)

Splittings

Fitting, socle, Hall	C₂₃×C₄₃ ⋊ C₂
derived, Sylow	C₄₃ ⋊ C₂×C₂₃

Subgroups

	subgroup	G/H
center, hypercenter	C₂₃	D₄₃
commutator, cosocle, hypocenter	C₄₃	C₂×C₂₃
Frattini	C₁	G
Fitting, socle	C₂₃×C₄₃	C₂
LCS	G ▷ C₄₃
UCS	C₁ ◁ C₂₃

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 66
transitive degree	μ_t(G) = 989

A minimal faithful permutation representation — 2 generators on 66 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66);(25,66)(26,65)(27,64)(28,63)(29,62)(30,61)(31,60)(32,59)(33,58)(34,57)(35,56)(36,55)(37,54)(38,53)(39,52)(40,51)(41,50)(42,49)(43,48)(44,47)(45,46)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₂₃×D₄₃, C₂×C₂₃×D₄₃, C₇×C₂₃×D₄₃, …
maximal normal subgroup of	D₂₃×D₄₃, C₂×C₂₃×D₄₃, C₇×C₂₃×D₄₃, …
maximal quotient of	C₂₃×Dic₄₃, C₂×C₂₃×D₄₃, C₇×C₂₃×D₄₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1978, 2);

C23×D43 #14520372