C₂₃×#2108 #15669727

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂×C₄×C₈×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#2108

Subgroups

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

184 conjugacy classes of subgroups; only the 168 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 168 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) = 59
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 59 points:

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

Conjugacy classes & character table

1840 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#7469, C₂₃×#7470, C₂₃×#12026, …
maximal normal subgroup of	C₂₃×#7469, C₂₃×#7470, C₂₃×#12026, …
maximal quotient of	C₂₃×#11399, C₂₃×#11401, C₁₆×M₁₆×C₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 840);