C₂₃×#2971 #15670590

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

Aliases

direct product

C₂₃×#2971

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	C₂×#41×C₂₃	C₄
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₂₃ ◁ G

402 conjugacy classes of subgroups; only the 276 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 276 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) = 1472

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

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₃×#9160, C₂₃×#9162, C₂₃×#9350, …
maximal normal subgroup of	C₂₃×#9160, C₂₃×#9162, C₂₃×#9350, …
maximal quotient of	C₂₃×#20480, C₂₃×#20494, Q₈×C₂₃×#97, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1703);