C₂₃×#2162 #15669781

order	2944
nilpotency class	2
isoclinism	isoclinic class of D₄
automorphism	?
homology	Abelianization (H₁) = C₂²×C₁₆×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#2162

Subgroups

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

160 conjugacy classes of subgroups; only the 120 normal subgroups are shown.

normal subgroups only

This group has 160 conjugacy classes of subgroups — too many to draw. Only its 120 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) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 47 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)(26,29)(27,28)(30,31)(32,33,34,37,35,38,40,43,36,39,41,44,42,45,46,47);(25,28)(29,31);(24,26,27,30)(25,29,28,31)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7142, C₂₃×#7144, C₂₃×#7145, …
maximal normal subgroup of	C₂₃×#7142, C₂₃×#7144, C₂₃×#7145, …
maximal quotient of	C₂₃×#12590, C₄×C₂₃×C₂²⋊C₁₆, C₄×C₂₃×C₄⋊C₁₆, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 894);