C₃×Dic₂₃ #63280

order	276
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₃×C₄ · Schur multiplier (H₂) = C₁

Aliases

direct product	C₃×Dic₂₃
unambiguous semidirect product	C₂₃⋊(C₃×C₄)

Splittings

derived, Sylow	C₂₃ ⋊ C₃×C₄
Hall	C₃×C₂₃ ⋊ C₄

Subgroups

	subgroup	G/H
center, hypercenter	C₂×C₃	D₂₃
commutator, hypocenter	C₂₃	C₃×C₄
Frattini	C₂	C₃×D₂₃
Fitting, socle, prime radical	C₂×C₃×C₂₃	C₂
cosocle	C₂×C₂₃	C₂×C₃
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₂×C₃

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 30
transitive degree	μ_t(G) = 276

A minimal faithful permutation representation — 2 generators on 30 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);(4,6,5,7)(9,30)(10,29)(11,28)(12,27)(13,26)(14,25)(15,24)(16,23)(17,22)(18,21)(19,20)

Conjugacy classes & character table

78 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	D₃×Dic₂₃, D₆₉⋊C₄, #10587772, …
maximal normal subgroup of	D₃×Dic₂₃, D₆₉⋊C₄, #10587772, …
maximal quotient of	C₃×C₂₃⋊C₈, C₂×C₃×Dic₂₃, C₉×Dic₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(276, 2);

C3×Dic23 #63280

Aliases

Splittings

Subgroups

Presentation

Conjugacy classes & character table

Relationships

GAP

C₃×Dic₂₃ #63280