C₂₃×#2979 #15670598

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂₃×#2979

Subgroups

	subgroup	G/H
center	C₂×C₄×C₂₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle	C₂²×C₂₃	C₂³×C₄
prime radical	C₂₃×#532	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

410 conjugacy classes of subgroups; only the 256 normal subgroups are shown.

normal subgroups only

This group has 410 conjugacy classes of subgroups — too many to draw. Only its 256 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) = 47
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 4 generators on 47 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)(27,29)(28,31)(32,33,35,38,36,39,42,45)(34,37,41,44,40,43,46,47);(24,26)(25,28)(27,31)(29,30)(32,34)(33,37)(35,41)(36,40)(38,44)(39,43)(42,46)(45,47);(26,31)(28,30)(32,34)(33,37)(35,41)(36,40)(38,44)(39,43)(42,46)(45,47);(25,29)(28,30)(34,40)(37,43)(41,46)(44,47)

Conjugacy classes & character table

1150 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂₃×#8934, C₂₃×#8935, C₂₃×#9067, …
maximal normal subgroup of	C₂₃×#8934, C₂₃×#8935, C₂₃×#9067, …
maximal quotient of	C₂₃×#20530, C₂₃×#20538, C₂₃×#20562, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1711);