C₂₃×#449 #13091998

order	1472
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#449

Subgroups

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

162 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 58 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) = 35
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 35 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)(29,33)(30,31)(34,35);(28,29)(30,33)(31,35)(32,34);(25,27)(28,30,32,31)(29,33,34,35)

Conjugacy classes & character table

437 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₂₃×#449, #15682612, #15682635, …
maximal subgroup of	C₂×C₂₃×#449, C₂₃×#3002, C₂₃×#3005, …
maximal normal subgroup of	C₂×C₂₃×#449, C₂₃×#3002, C₂₃×#3005, …
maximal quotient of	C₂₃×#1597, C₂₃×#1600, C₂₃×#1609, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1472, 130);