C₂₃×#2168 #15669787

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2168

Subgroups

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

164 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 1472

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)(24,25)(26,27)(28,29,31,35,32,30,37,38,33,36,40,43,41,39,34,42);(25,27);(28,30,31,38,32,36,37,43,33,39,40,42,41,29,34,35)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₃×#2168, C₂₃×#33432, C₂₃×#33433, …
maximal normal subgroup of	C₂×C₂₃×#2168, C₂₃×#33432, C₂₃×#33433, …
maximal quotient of	C₂₃×#12038, C₂₃×#12049, C₂₃×#12050, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 900);