C₂₃×#1440 #15669059

order	2944
nilpotency class	2
isoclinism	isoclinic class of #392
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#1440

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₂₃	C₂³
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂⁴	C₂³×C₂₃
prime radical	C₂⁵×C₂₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₃ ◁ G

736 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 736 conjugacy classes of subgroups — too many to draw. Only its 216 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 — 3 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)(29,31)(32,33,34,35)(36,37,39,38);(25,27)(29,31)(37,38);(24,25)(26,27)(28,29)(30,31)(32,33)(34,35)(36,38,39,37)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7324, C₂₃×#8535, C₂×C₂₃×#1440, …
maximal normal subgroup of	C₂₃×#7324, C₂₃×#8535, C₂×C₂₃×#1440, …
maximal quotient of	C₂₃×#7555, C₂₃×#7556, C₂₃×#11147, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 172);