C₂₃×#1471 #15669090

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1468
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂³

Aliases

direct product

C₂₃×#1471

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×C₂²⋊C₄
commutator	C₂³	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂×C₂₃×#121	C₂
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂³×C₄×C₂₃ ◁ G

322 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 96 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)(32,33,35,39,36,37,34,38);(24,26)(25,28)(27,31)(29,30)(33,37)(34,35);(32,34,36,35)(33,38,37,39)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8465, C₂₃×#8466, C₂₃×#8536, …
maximal normal subgroup of	C₂₃×#8465, C₂₃×#8466, C₂₃×#8536, …
maximal quotient of	C₂₃×#7664, C₂₃×#7667, C₂₃×#7670, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 203);