C₂₃×#3059 #15670678

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3057
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#3059

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂×#41×C₂₃	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×#41×C₂₃ ◁ G

460 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 460 conjugacy classes of subgroups — too many to draw. Only its 200 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) = 59
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 59 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)(28,29,33,37)(30,38,42,52)(31,35,43,49)(32,45,39,36)(34,46,48,41)(40,51,54,59)(44,56,53,50)(47,57,58,55);(28,30,39,46,33,42,32,41)(29,34,45,52,37,48,36,38)(31,40,53,57,43,54,44,55)(35,47,56,59,49,58,50,51);(25,27)(28,31)(29,35)(30,40)(32,44)(33,43)(34,47)(36,50)(37,49)(38,51)(39,53)(41,55)(42,54)(45,56)(46,57)(48,58)(52,59);(31,43)(35,49)(40,54)(44,53)(47,58)(50,56)(51,59)(55,57)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#11869, C₂₃×#11871, C₂₃×#13075, …
maximal normal subgroup of	C₂₃×#11869, C₂₃×#11871, C₂₃×#13075, …
maximal quotient of	C₂₃×#19188, C₂₃×#19193, C₂₃×#19199, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1791);