C₂₃×#2164 #15669783

order	2944
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂²×C₈×C₂₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₂₃×#2164

Subgroups

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

138 conjugacy classes of subgroups; only the 96 normal subgroups are shown.

normal subgroups only

This group has 138 conjugacy classes of subgroups — too many to draw. Only its 96 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) = 63
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 63 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)(26,29)(27,28)(30,31)(32,33,35,39,36,40,45,51,37,41,46,52,47,53,57,61)(34,38,43,49,44,50,56,60,42,48,54,58,55,59,62,63);(25,28)(29,31)(32,34)(33,38)(35,43)(36,44)(37,42)(39,49)(40,50)(41,48)(45,56)(46,54)(47,55)(51,60)(52,58)(53,59)(57,62)(61,63);(24,26,27,30)(25,29,28,31)(34,42)(38,48)(43,54)(44,55)(49,58)(50,59)(56,62)(60,63)

Conjugacy classes & character table

1288 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₂₃×#2164, C₂₃×#33419, C₂₃×#33420, …
maximal normal subgroup of	C₂×C₂₃×#2164, C₂₃×#33419, C₂₃×#33420, …
maximal quotient of	C₂₃×#12592, C₂₃×#12600, C₂₃×#12654, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 896);