C₃²×C₂²⋊D₂₃ #13110246

order	1656
isoclinism	isoclinic class of Dic₄₆
automorphism	?
homology	Abelianization (H₁) = C₂²×C₃² · Schur multiplier (H₂) = C₂×C₃

supersolvable
metabelian
solvable
monomial

Aliases

direct product

C₃²×C₂²⋊D₂₃

Splittings

Fitting	C₂²×C₃²×C₂₃ ⋊ C₂
Hall	C₃²×C₂₃ ⋊ D₄
Sylow	C₂₃ ⋊ C₃²×D₄

Subgroups

	subgroup	G/H
center	C₂×C₃²	C₂×D₂₃
commutator, cosocle	C₂×C₂₃	C₂²×C₃²
Frattini	C₂	C₂×C₃²×D₂₃
Fitting	C₂²×C₃²×C₂₃	C₂
socle	C₂×C₃²×C₂₃	C₂²
hypercenter	C₂²×C₃²	D₂₃
hypocenter	C₂₃	C₃²×D₄
LCS	G ▷ C₂×C₂₃ ▷ C₂₃
UCS	C₁ ◁ C₂×C₃² ◁ C₂²×C₃²

96 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 828

A minimal faithful permutation representation — 2 generators on 33 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1656, 84);

C32×C22⋊D23 #13110246