C₂₃×#3414 #15671033

order	2944
nilpotency class	4
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₂₃×#3414

Subgroups

	subgroup	G/H
center	C₄×C₂₃	C₂×D₈
commutator, Frattini, cosocle	C₈	C₂⁴×C₂₃
socle	C₂×C₂₃	C₂²×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₂₃ ◁ C₂²×C₄×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

364 conjugacy classes of subgroups; only the 180 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 180 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)(26,35)(27,33)(28,40)(29,44)(30,32)(31,37)(34,42)(36,52)(38,51)(39,49)(41,47)(43,54)(45,50)(46,53)(48,55);(24,26)(25,31)(27,36)(28,41)(29,45)(30,38)(32,46)(33,47)(34,50)(35,40)(37,42)(39,53)(43,55)(44,48)(49,52)(51,54);(25,32)(31,46)(33,44)(34,49)(35,51)(40,54)(47,48)(50,52);(24,27,30,29)(25,33,32,44)(26,36,38,45)(28,39,43,42)(31,47,46,48)(34,40,49,54)(35,52,51,50)(37,41,53,55)

Conjugacy classes & character table

736 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#13021, C₂₃×#13024, C₂₃×#13027, …
maximal normal subgroup of	C₂₃×#13021, C₂₃×#13024, C₂₃×#13027, …
maximal quotient of	C₂₃×#33380, C₂₃×#33409, C₂₃×#33451, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 2146);