C₂₃×#2249 #15669868

order	2944
nilpotency class	4
isoclinism	isoclinic class of #2215
automorphism	?
homology	Abelianization (H₁) = C₂³×C₂₃ · Schur multiplier (H₂) = C₂×C₄

Aliases

direct product

C₂₃×#2249

Subgroups

	subgroup	G/H
center, socle	C₂²×C₂₃	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂³×C₂₃
prime radical	C₂×C₂₃×D₁₆	C₂
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₂₃ ◁ C₄²×C₂₃ ◁ C₄×C₈×C₂₃ ◁ G

184 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 184 conjugacy classes of subgroups — too many to draw. Only its 72 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) = 59
transitive degree	μ_t(G) = 1472

A minimal faithful permutation representation — 3 generators on 59 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23)(25,27)(28,29)(30,38)(31,43)(32,35)(33,46)(34,40)(36,39)(37,44)(41,50)(42,57)(45,58)(47,56)(48,59)(49,54)(51,53)(52,55);(28,30,39,53,33,42,45,56,32,41,54,59,44,55,31,40)(29,34,43,52,37,48,49,50,35,47,58,57,46,51,36,38);(24,25,26,27)(29,35)(34,47)(36,49)(37,46)(38,50)(43,58)(48,51)(52,57)

Conjugacy classes & character table

874 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#7446, C₂₃×#7447, C₂₃×#13689, …
maximal normal subgroup of	C₂₃×#7446, C₂₃×#7447, C₂₃×#13689, …
maximal quotient of	C₂₃×#12503, C₂₃×#12504, C₂₃×#12505, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 981);