C₂₃×#1790 #15669409

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#1790

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	#120
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂⁴	C₂³×C₂₃
prime radical	C₂×C₂₃×H(5,𝔽₂)	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂⁴×C₂₃ ◁ G

670 conjugacy classes of subgroups; only the 136 normal subgroups are shown.

normal subgroups only

This group has 670 conjugacy classes of subgroups — too many to draw. Only its 136 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) = 35
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 35 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)(30,34,35,32)(31,33);(28,30)(29,32)(31,35)(33,34);(25,27)(28,29)(30,32)(31,33)(34,35)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13041, C₂₃×#13042, C₂₃×#13043, …
maximal normal subgroup of	C₂₃×#13041, C₂₃×#13042, C₂₃×#13043, …
maximal quotient of	C₂₃×#8316, C₂₃×#8317, C₂₃×#8346, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 522);