C₂₃×#3022 #15670641

order	2944
nilpotency class	3
isoclinism	isoclinic class of #3019
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂₃×#3022

Subgroups

	subgroup	G/H
center, socle	C₂×C₂₃	C₂×#120
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
prime radical	C₂₃×#585	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ G

704 conjugacy classes of subgroups; only the 212 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 212 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)(24,25,30,35)(26,36,39,48)(27,32,41,47)(28,34,29,33)(31,42,45,38)(37,51,54,50)(40,49,43,46)(44,52,55,53);(24,26)(25,31)(27,37)(28,38)(29,42)(30,39)(32,44)(33,36)(34,48)(35,45)(40,52)(41,54)(43,53)(46,50)(47,55)(49,51);(24,27)(25,32)(26,37)(28,40)(29,43)(30,41)(31,44)(33,46)(34,49)(35,47)(36,50)(38,52)(39,54)(42,53)(45,55)(48,51);(24,28,30,29)(25,33,35,34)(26,38,39,42)(27,40,41,43)(31,36,45,48)(32,46,47,49)(37,52,54,53)(44,50,55,51)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13355, C₂₃×#13356, C₂₃×#13361, …
maximal normal subgroup of	C₂₃×#13355, C₂₃×#13356, C₂₃×#13361, …
maximal quotient of	C₂₃×#18136, C₂₃×#18140, C₂₃×#18146, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1754);