C₁₁×#2483 #13065321

order	1408
nilpotency class	2
isoclinism	isoclinic class of #2403
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₁ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₁×#2483

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₁	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₁
prime radical	C₂⁵×C₁₁	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₁ ◁ G

700 conjugacy classes of subgroups; only the 216 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 216 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) = 31
transitive degree	μ_t(G) = 352

A minimal faithful permutation representation — 4 generators on 31 points:

(1,2,3,4,5,6,7,8,9,10,11)(13,15)(16,17,20,18)(19,22,23,21)(25,28)(26,30);(17,18)(21,22)(24,25)(26,29)(27,28)(30,31);(12,13)(14,15)(16,18,20,17)(19,22,23,21)(24,26,27,30)(25,29,28,31);(16,19)(17,21)(18,22)(20,23)(24,25)(26,29)(27,28)(30,31)

Conjugacy classes & character table

418 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#14651698, #14651708, #14656732, …
maximal subgroup of	C₁₁×#9500, C₁₁×#9502, C₁₁×#10338, …
maximal normal subgroup of	C₁₁×#9500, C₁₁×#9502, C₁₁×#10338, …
maximal quotient of	C₁₁×#13869, C₁₁×#13992, C₁₁×#14040, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1408, 1215);