C₂₃×#3020 #15670639

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

Aliases

direct product

C₂₃×#3020

Subgroups

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

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

normal subgroups only

This group has 698 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)(26,34)(27,31)(28,40)(29,32)(30,36)(33,43)(35,51)(37,48)(38,49)(39,46)(41,45)(42,47)(44,52)(50,53)(54,55);(24,26)(25,30)(27,35)(28,41)(29,37)(31,44)(32,45)(33,48)(34,40)(36,43)(38,54)(39,53)(42,52)(46,55)(47,50)(49,51);(24,27,29,39)(25,31,32,46)(26,35,37,53)(28,42,43,38)(30,44,45,55)(33,49,40,47)(34,50,48,51)(36,54,41,52);(25,32)(30,45)(31,46)(33,40)(34,48)(44,55)(47,49)(50,51)

Conjugacy classes & character table

667 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#23874, C₂₃×#23875, C₂₃×#23893, …
maximal normal subgroup of	C₂₃×#23874, C₂₃×#23875, C₂₃×#23893, …
maximal quotient of	C₂₃×#18134, C₂₃×#18139, C₂₃×#18142, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1752);