C₂²×C₂₃×#125 #15671056

order	2944
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₂₃ · Schur multiplier (H₂) = C₂⁸

Aliases

direct product

C₂²×C₂₃×#125

Subgroups

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

1192 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 5 generators on 43 points:

(1,2)(21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(3,4);(7,11)(9,12)(13,14,16,18)(15,17,19,20);(5,6,8,10)(7,9,11,12)(13,14)(15,17)(16,18)(19,20);(5,7)(6,9)(8,11)(10,12)(13,15,16,19)(14,17,18,20)

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#8306, C₂₃×#8335, C₂₃×#8554, …
maximal normal subgroup of	C₂₃×#8306, C₂₃×#8335, C₂₃×#8554, …
maximal quotient of	C₂²×C₂₃×#382, C₂²×C₂₃×#387, C₂²×C₂₃×#389, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2169);

C22×C23×#125 #15671056