C₂₃×#1379 #15668998

order	2944
nilpotency class	3
isoclinism	isoclinic class of D₈
automorphism	?
homology	Abelianization (H₁) = C₄×C₈×C₂₃ · Schur multiplier (H₂) = C₂²

Aliases

direct product

C₂₃×#1379

Subgroups

	subgroup	G/H
center	C₂×C₈×C₂₃	D₄
commutator	C₄	C₄×C₈×C₂₃
Frattini, cosocle	C₂²×C₈	C₂²×C₂₃
socle	C₂²×C₂₃	C₂²⋊C₈
prime radical	C₂³×C₂₃	M₁₆
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₈×C₂₃ ◁ C₂²×C₈×C₂₃ ◁ G

136 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 88 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 — 2 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)(28,29,32,37,33,38,47,55,34,39,48,56,31,36,45,53)(30,40,42,57,41,51,58,54,43,52,46,59,44,35,49,50);(24,25,26,27)(28,30)(29,35)(31,44)(32,46)(33,41)(34,43)(36,52)(37,54)(38,40)(39,51)(42,48)(45,58)(47,49)(50,56)(53,57)(55,59)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂×C₂₃×#1379, C₂₃×#12554, C₂₃×#12597, …
maximal normal subgroup of	C₂×C₂₃×#1379, C₂₃×#12554, C₂₃×#12597, …
maximal quotient of	C₂₃×#7141, C₂₃×#7144, C₂₃×#7147, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 111);