C₂₃×#2098 #15669717

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2010
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2098

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#127
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
socle	C₂×C₂₃	#399
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

210 conjugacy classes of subgroups; only the 80 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 80 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)(24,25,28,33,29,34,30,44)(26,35,37,47,39,51,38,31)(27,40,42,50,43,32,45,49)(36,52,41,55,53,48,54,46);(24,26,30,37,29,39,28,38)(25,31,44,35,34,47,33,51)(27,41,45,53,43,54,42,36)(32,48,50,46,40,52,49,55);(24,27)(25,32)(26,36)(28,42)(29,43)(30,45)(31,46)(33,49)(34,40)(35,52)(37,41)(38,54)(39,53)(44,50)(47,55)(48,51)

Conjugacy classes & character table

598 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7438, C₂₃×#7439, C₂₃×#12301, …
maximal normal subgroup of	C₂₃×#7438, C₂₃×#7439, C₂₃×#12301, …
maximal quotient of	C₂₃×#10659, C₂₃×#10660, C₂₃×#10661, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 830);