C₂₃×#2148 #15669767

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

Aliases

direct product

C₂₃×#2148

Subgroups

	subgroup	G/H
center	C₄×C₂₃	#102
commutator	C₈	C₂²×C₄×C₂₃
Frattini, cosocle	C₂×C₈	C₂³×C₂₃
socle	C₂×C₂₃	C₂×#102
prime radical	C₂×C₂₃×#135	C₂
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

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

normal subgroups only

This group has 220 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)(24,25,27,31,29,34,41,33)(26,35,38,49,39,52,36,51)(28,42,40,32,44,48,53,50)(30,43,46,37,47,54,45,55);(24,26)(25,30)(27,36)(28,43)(29,39)(31,45)(32,49)(33,46)(34,47)(35,48)(37,53)(38,41)(40,55)(42,52)(44,54)(50,51);(24,27,29,41)(25,31,34,33)(26,36,39,38)(28,40,44,53)(30,45,47,46)(32,48,50,42)(35,51,52,49)(37,43,55,54)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12646, C₂₃×#12651, C₂₃×#12740, …
maximal normal subgroup of	C₂₃×#12646, C₂₃×#12651, C₂₃×#12740, …
maximal quotient of	C₂₃×#11597, C₂₃×#11598, C₂₃×#11651, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 880);