C₂₃×#1521 #15669140

order	2944
nilpotency class	3
isoclinism	isoclinic class of #1504
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#1521

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×C₂²⋊C₄
commutator	C₂×C₄	C₂²×C₄×C₂₃
Frattini, cosocle	C₂²×C₄	C₂³×C₂₃
prime radical	C₂₃×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

218 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 88 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)(25,30,32,44)(26,35)(27,40)(31,46,47,52)(33,45,34,41)(36,51,48,43)(38,54)(39,50)(42,53)(49,55);(24,25)(26,36)(27,41)(28,33)(29,34)(30,42)(31,39)(32,37)(35,47)(38,51)(40,44)(43,54)(45,53)(46,55)(48,50)(49,52);(24,26,37,50)(25,31,32,47)(27,38,53,54)(28,39,29,35)(30,43,44,51)(33,36,34,48)(40,55,42,49)(41,46,45,52)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#8500, C₂₃×#8501, C₂₃×#8502, …
maximal normal subgroup of	C₂₃×#8500, C₂₃×#8501, C₂₃×#8502, …
maximal quotient of	C₂₃×#7580, C₂₃×#7581, C₂₃×#7584, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 253);