C₂₃×#2889 #15670508

order	2944
nilpotency class	3
isoclinism	isoclinic class of #2883
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#2889

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂²×C₂²⋊C₄
commutator	C₂²	C₂³×C₄×C₂₃
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂×C₂₃×2₋¹⁺⁴	C₂
LCS	G ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂×#41×C₂₃ ◁ G

704 conjugacy classes of subgroups; only the 340 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 340 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 — 4 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)(24,25,28,33,29,32,41,46)(26,34,36,47,37,30,40,43)(27,31,39,45,38,44,51,54)(35,48,50,55,49,42,52,53);(24,26,29,37)(25,30,32,34)(27,35,38,49)(28,40,41,36)(31,42,44,48)(33,47,46,43)(39,52,51,50)(45,55,54,53);(24,27)(25,31)(26,35)(28,39)(29,38)(30,42)(32,44)(33,45)(34,48)(36,50)(37,49)(40,52)(41,51)(43,53)(46,54)(47,55);(27,38)(31,44)(35,49)(39,51)(42,48)(45,54)(50,52)(53,55)

Conjugacy classes & character table

943 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13096, C₂₃×#13098, C₂₃×#21780, …
maximal normal subgroup of	C₂₃×#13096, C₂₃×#13098, C₂₃×#21780, …
maximal quotient of	C₂₃×#17351, C₂₃×#17352, C₂₃×#17368, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1621);