C₂₃×#1735 #15669354

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₂₃×#1735

Subgroups

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

424 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 232 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) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 47 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)(26,27)(28,29,30,31)(32,33)(34,42)(35,39)(36,40)(37,41)(38,43)(44,47)(45,46);(25,27)(32,34,36,44,37,45,35,43)(33,38,39,46,41,47,40,42);(32,35,37,36)(33,39,41,40)(34,43,45,44)(38,46,47,42)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#7260, C₂₃×#7262, C₂₃×#10706, …
maximal normal subgroup of	C₂₃×#7260, C₂₃×#7262, C₂₃×#10706, …
maximal quotient of	C₂₃×#7872, C₂₃×#7875, C₂₃×#7878, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 467);