C₂₃×#3531 #15671150

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₃ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂₃×#3531

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁵×C₂₃
socle	C₂²×C₂₃	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

930 conjugacy classes of subgroups; only the 760 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 760 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) = 1472

A minimal faithful permutation representation — 5 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)(26,32)(27,31)(28,30)(29,33)(34,38)(35,37)(36,39)(40,41)(42,45)(43,50)(44,47)(46,52)(48,55)(49,54)(51,53);(24,26)(25,29)(27,34)(28,33)(30,32)(31,36)(35,39)(37,38)(40,42,44,49)(41,45,47,54)(43,51,52,48)(46,55,50,53);(26,33)(29,32)(34,39)(36,38)(40,43,44,52)(41,46,47,50)(42,48,49,51)(45,53,54,55);(25,30)(26,33)(31,37)(34,39)(41,47)(45,54)(46,50)(53,55);(24,27,28,35)(25,31,30,37)(26,34,33,39)(29,36,32,38)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8505, C₂₃×#18990, C₂₃×#18991, …
maximal normal subgroup of	C₂₃×#8505, C₂₃×#18990, C₂₃×#18991, …
maximal quotient of	C₂₃×#34348, C₂₃×#34350, C₄×C₂₃×#562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2263);