C₂₃×#536 #13092085

order	1472
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#536

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₂₃
prime radical	C₂×#41×C₂₃	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ G

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

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 162 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) = 43
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(29,33)(30,36)(31,39)(41,43);(28,29,32,33)(30,37,36,34)(31,35,39,40)(38,43,42,41);(24,25)(26,27)(28,30,32,36)(29,34,33,37)(31,38,39,42)(35,41,40,43);(28,31)(29,35)(30,38)(32,39)(33,40)(34,41)(36,42)(37,43)

Conjugacy classes & character table

506 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15673920, #15673935, #15673950, …
maximal subgroup of	C₂₃×#1909, C₂₃×#1912, C₂₃×#1915, …
maximal normal subgroup of	C₂₃×#1909, C₂₃×#1912, C₂₃×#1915, …
maximal quotient of	C₂₃×#2310, C₂₃×#2311, C₂₃×#2317, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1472, 217);