C₂×C₂₃×#499 #15670777

order	2944
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₂×C₂₃×#499

Subgroups

	subgroup	G/H
center, socle, prime radical	C₂³×C₂₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ C₂×C₄²×C₂₃ ◁ G

360 conjugacy classes of subgroups; only the 232 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 232 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) = 49
transitive degree	μ_t(G) = 2944

A minimal faithful permutation representation — 4 generators on 49 points:

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

Conjugacy classes & character table

1012 conjugacy classes — view the full character table.

Relationships

maximal subgroup of	C₂₃×#9788, C₂₃×#9792, C₂×C₂₃×#1363, …
maximal normal subgroup of	C₂₃×#9788, C₂₃×#9792, C₂×C₂₃×#1363, …
maximal quotient of	C₂×C₂₃×#1846, C₂×C₂₃×#1941, C₂×C₂₃×#1942, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(2944, 1890);