C₂₃×#2171 #15669790

order	2944
nilpotency class	3
isoclinism	isoclinic class of AGL(1,ℤ/8)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2171

Subgroups

	subgroup	G/H
center	C₈×C₂₃	C₂×D₄
commutator	C₄	C₂²×C₈×C₂₃
Frattini, cosocle	C₂×C₈	C₂³×C₂₃
socle	C₂×C₂₃	C₈×D₄
prime radical	C₂₃×#135	C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₈×C₂₃ ◁ C₂×C₁₆×C₂₃ ◁ G

144 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 92 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) = 55
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 55 points:

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12068, C₂₃×#12465, C₂₃×#12466, …
maximal normal subgroup of	C₂₃×#12068, C₂₃×#12465, C₂₃×#12466, …
maximal quotient of	C₂₃×#12038, C₂₃×#12049, C₂₃×#12050, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 903);