C₂₃×#2275 #15669894

order	2944
nilpotency class	2
isoclinism	isoclinic class of H(5,𝔽₂)
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄²×C₂₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₂₃×#2275

Subgroups

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

780 conjugacy classes of subgroups; only the 520 normal subgroups are shown.

normal subgroups only

This group has 780 conjugacy classes of subgroups — too many to draw. Only its 520 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) = 39
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 39 points:

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

Conjugacy classes & character table

1564 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#9323, C₂₃×#9325, C₂₃×#17547, …
maximal normal subgroup of	C₂₃×#9323, C₂₃×#9325, C₂₃×#17547, …
maximal quotient of	C₂₃×#13749, C₂₃×#13750, C₂₃×#13782, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1007);