C₁₃×#2383 #13111441

order	1664
nilpotency class	2
isoclinism	isoclinic class of #560
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#2383

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator	C₂²	C₂³×C₄×C₁₃
Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂⁴×C₁₃	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

456 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 264 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) = 33
transitive degree	μ_t(G) = 832

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13)(14,15,16,17)(19,22)(20,24)(26,27,30,28)(29,32,33,31);(19,22)(23,25)(27,28)(29,33);(18,19)(20,23)(21,22)(24,25)(26,28,30,27)(29,32,33,31);(18,20,21,24)(19,23,22,25)(26,29)(27,31)(28,32)(30,33)

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₃×#2383, #16025588, #16025606, …
maximal subgroup of	C₂×C₁₃×#2383, C₁₃×#34350, C₄×C₁₃×#560, …
maximal normal subgroup of	C₂×C₁₃×#2383, C₁₃×#34350, C₄×C₁₃×#560, …
maximal quotient of	C₁₃×#13830, C₁₃×#13831, C₁₃×#13833, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1115);