C₂₃×#2170 #15669789

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2170

Subgroups

	subgroup	G/H
center	C₁₆×C₂₃	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 ◁ C₁₆×C₂₃ ◁ C₂×C₁₆×C₂₃ ◁ G

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

normal subgroups only

This group has 146 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)(24,25,29,33,28,34,43,51,30,35,45,52,44,32,48,50)(26,36,38,41,39,47,53,42,40,49,54,55,37,31,46,27);(24,26)(25,31)(27,33)(28,39)(29,38)(30,40)(32,49)(34,36)(35,47)(37,44)(41,51)(42,52)(43,53)(45,54)(46,48)(50,55);(24,27,29,36,28,41,43,47,30,42,45,49,44,55,48,31)(25,26,33,38,34,39,51,53,35,40,52,54,32,37,50,46)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7381, C₂₃×#7382, C₂₃×#12046, …
maximal normal subgroup of	C₂₃×#7381, C₂₃×#7382, C₂₃×#12046, …
maximal quotient of	C₁₆×D₈×C₂₃, C₂₃×#12039, C₁₆×SD₁₆×C₂₃, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 902);