C₂₃×#1772 #15669391

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#1772

Subgroups

	subgroup	G/H
center	C₂×C₈×C₂₃	D₄
commutator	C₄	C₂×C₄²×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂²×C₂₃	C₄×D₄
prime radical	C₂³×C₂₃	#41
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

232 conjugacy classes of subgroups; only the 152 normal subgroups are shown.

normal subgroups only

This group has 232 conjugacy classes of subgroups — too many to draw. Only its 152 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(29,33,35,38)(34,40,41,42);(24,25,26,27)(28,29)(30,34)(31,38)(32,35)(33,39)(36,42)(37,41)(40,43);(28,30,31,36,32,37,39,43)(29,34,38,42,35,41,33,40)

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7179, C₂₃×#7180, C₂₃×#7181, …
maximal normal subgroup of	C₂₃×#7179, C₂₃×#7180, C₂₃×#7181, …
maximal quotient of	C₂₃×#8266, C₂₃×#8267, C₂₃×#8270, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 504);