C₂₃×#1465 #15669084

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1462
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1465

Subgroups

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

316 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 736

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)(24,25)(26,30,31,28)(27,29)(32,33,35,37,36,38,34,39);(24,26)(25,28)(27,31)(29,30);(32,34,36,35)(33,37,38,39)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7247, C₂₃×#7249, C₂₃×#7321, …
maximal normal subgroup of	C₂₃×#7247, C₂₃×#7249, C₂₃×#7321, …
maximal quotient of	C₂₃×#7616, C₂₃×#7617, C₂₃×#7620, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 197);