C₂×C₄×Q₁₆×C₂₃ #15670557

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂×C₄×Q₁₆×C₂₃

Subgroups

	subgroup	G/H
center	C₂²×C₄×C₂₃	D₄
commutator	C₄	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle, prime radical	C₂³×C₂₃	C₂×D₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

488 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 2944

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);(7,8,9,10,11,12,13,14)(15,22,21,20,19,18,17,16);(7,15,11,19)(8,16,12,20)(9,17,13,21)(10,18,14,22)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#8946, C₂₃×#8950, C₂₃×#9656, …
maximal normal subgroup of	C₂₃×#8946, C₂₃×#8950, C₂₃×#9656, …
maximal quotient of	C₂×C₈×Q₁₆×C₂₃, C₂×C₂₃×#1584, C₂×C₂₃×#1591, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1670);

C2×C4×Q16×C23 #15670557