C₂₃×#2155 #15669774

order	2944
nilpotency class	4
isoclinism	isoclinic class of #365
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#2155

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#106
commutator	C₈	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₈	C₂³×C₂₃
socle	C₂×C₂₃	C₂×#106
prime radical	C₂³×C₂₃	SD₁₆
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

144 conjugacy classes of subgroups; only the 100 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 100 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) = 55
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 3 generators on 55 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)(26,35,38,49)(27,32)(28,41)(29,44)(30,34)(31,37,46,51)(33,42)(36,48,39,53)(40,47)(43,54)(45,50,55,52);(24,26,28,37,29,39,42,52,30,38,43,51,27,36,40,50)(25,31,33,35,32,45,41,48,34,46,47,49,44,55,54,53);(24,27,30,29)(25,32,34,44)(26,36,38,39)(28,40,43,42)(31,45,46,55)(33,41,47,54)(35,48,49,53)(37,50,51,52)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12668, C₂₃×#12678, C₂₃×#12832, …
maximal normal subgroup of	C₂₃×#12668, C₂₃×#12678, C₂₃×#12832, …
maximal quotient of	C₂₃×#11999, C₂₃×#12000, C₂₃×#12019, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 887);