C₂₃×#2145 #15669764

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

Aliases

direct product

C₂₃×#2145

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

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

normal subgroups only

This group has 224 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)(26,35,38,52)(27,31)(28,42)(29,34)(30,37,46,54)(32,40)(33,41)(36,51,39,48)(43,50,55,45)(44,47)(49,53);(24,26)(25,30)(27,36)(28,43)(29,38)(31,45)(32,48)(33,50)(34,46)(35,47)(37,53)(39,41)(40,54)(42,52)(44,55)(49,51);(24,27,29,41)(25,31,34,33)(26,36,38,39)(28,40,44,53)(30,45,46,50)(32,47,49,42)(35,51,52,48)(37,43,54,55)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#12646, C₂₃×#12649, C₂₃×#12741, …
maximal normal subgroup of	C₂₃×#12646, C₂₃×#12649, C₂₃×#12741, …
maximal quotient of	C₂₃×#11597, C₂₃×#11599, C₂₃×#11600, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 877);