C₂₃×#3417 #15671036

order	2944
nilpotency class	4
isoclinism	isoclinic class of #3415
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#3417

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂²×D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₂₃
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ #41×C₂₃ ◁ C₂₃×#131 ◁ G

350 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 180 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) = 87
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 87 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(24,25,30,35)(26,36,40,64)(27,32,41,55)(28,44,48,62)(29,49,46,34)(31,51,54,38)(33,58,60,47)(37,63,65,85)(39,68,50,59)(42,71,69,84)(43,74,70,57)(45,61,76,53)(52,77,78,66)(56,81,80,73)(67,86,75,82)(72,83,87,79);(24,26,30,40)(25,31,35,54)(27,37,41,65)(28,45,48,76)(29,50,46,39)(32,52,55,78)(33,59,60,68)(34,61,49,53)(36,62,64,44)(38,58,51,47)(42,72,69,87)(43,75,70,67)(56,82,80,86)(57,83,74,79)(63,84,85,71)(66,81,77,73);(24,27)(25,32)(26,37)(28,42)(29,43)(30,41)(31,52)(33,56)(34,57)(35,55)(36,63)(38,66)(39,67)(40,65)(44,71)(45,72)(46,70)(47,73)(48,69)(49,74)(50,75)(51,77)(53,79)(54,78)(58,81)(59,82)(60,80)(61,83)(62,84)(64,85)(68,86)(76,87);(27,41)(32,55)(37,65)(42,69)(43,70)(52,78)(56,80)(57,74)(63,85)(66,77)(67,75)(71,84)(72,87)(73,81)(79,83)(82,86)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13670, C₂₃×#13672, C₂₃×#33855, …
maximal normal subgroup of	C₂₃×#13670, C₂₃×#13672, C₂₃×#33855, …
maximal quotient of	C₂₃×#33382, C₂₃×#33410, C₂₃×#33455, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2149);