C₂×C₂₃×#416 #15670511

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₂₃×#416

Subgroups

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

792 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 45 points:

(1,2)(23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45);(3,4,5,6)(7,8)(9,16)(10,14)(11,19)(12,15)(13,17)(18,21)(20,22);(7,9)(8,13)(10,17)(11,20)(12,18)(14,21)(15,22)(16,19);(7,10,12,11)(8,14,15,19)(9,17,18,20)(13,21,22,16)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#10779, C₂₃×#10782, C₂₃×#10791, …
maximal normal subgroup of	C₂₃×#10779, C₂₃×#10782, C₂₃×#10791, …
maximal quotient of	C₂×C₂₃×#1476, C₂×C₂₃×#1488, C₂₃×#17443, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1624);

C2×C23×#416 #15670511