C₂₃×#3025 #15670644

order	2944
nilpotency class	3
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#3025

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#120
commutator, Frattini, cosocle	C₂³	C₂⁴×C₂₃
socle	C₂×C₂₃	C₂×#120
LCS	G ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

766 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 766 conjugacy classes of subgroups — too many to draw. Only its 212 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) = 368

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

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13045, C₂₃×#13046, C₂₃×#21483, …
maximal normal subgroup of	C₂₃×#13045, C₂₃×#13046, C₂₃×#21483, …
maximal quotient of	C₂₃×#18122, C₂₃×#18123, C₂₃×#18124, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1757);