D₂₃×C₄₇ #14524183

order	2162
isoclinism	isoclinic class of D₂₃
automorphism	?
homology	Abelianization (H₁) = C₂×C₄₇ · Schur multiplier (H₂) = C₁

Aliases

direct product	D₂₃×C₄₇
unambiguous semidirect product	C₂₃⋊(C₂×C₄₇)

Splittings

Fitting, socle, Hall	C₂₃×C₄₇ ⋊ C₂
derived, Sylow	C₂₃ ⋊ C₂×C₄₇

Subgroups

	subgroup	G/H
center, hypercenter	C₄₇	D₂₃
commutator, cosocle, hypocenter	C₂₃	C₂×C₄₇
Frattini	C₁	G
Fitting, socle	C₂₃×C₄₇	C₂
LCS	G ▷ C₂₃
UCS	C₁ ◁ C₄₇

8 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 70
transitive degree	μ_t(G) = 1081

A minimal faithful permutation representation — 2 generators on 70 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70);(2,23)(3,22)(4,21)(5,20)(6,19)(7,18)(8,17)(9,16)(10,15)(11,14)(12,13)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	D₂₃×D₄₇, C₂×D₂₃×C₄₇, C₅×D₂₃×C₄₇, …
maximal normal subgroup of	D₂₃×D₄₇, C₂×D₂₃×C₄₇, C₅×D₂₃×C₄₇, …
maximal quotient of	C₄₇×Dic₂₃, C₂×D₂₃×C₄₇, C₅×D₂₃×C₄₇, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2162, 3);

D23×C47 #14524183