C₂₃×#2315 #15669934

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#2315

Subgroups

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

816 conjugacy classes of subgroups; only the 360 normal subgroups are shown.

normal subgroups only

This group has 816 conjugacy classes of subgroups — too many to draw. Only its 360 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 — 4 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)(25,27)(28,29,30,31)(32,33)(34,36)(35,38)(37,39);(33,34)(37,38);(24,25,26,27)(32,34,36,33)(35,38,39,37);(32,35)(33,37)(34,38)(36,39)

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8756, C₂₃×#8853, C₂₃×#8854, …
maximal normal subgroup of	C₂₃×#8756, C₂₃×#8853, C₂₃×#8854, …
maximal quotient of	C₂₃×#13778, C₂₃×#13782, C₂₃×#13794, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1047);