C₁₃×#2860 #13111918

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2846
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#2860

Subgroups

	subgroup	G/H
center, socle	C₂³×C₁₃	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₁₃
prime radical	C₂²×D₄×C₁₃	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₁₃ ◁ G

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

normal subgroups only

This group has 516 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) = 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)(15,17)(19,20)(23,24)(28,31)(29,33);(18,19,22,20)(21,23,25,24)(26,27,30,32)(28,29,31,33);(14,15,16,17)(18,20,22,19)(21,24,25,23)(26,28,30,31)(27,29,32,33);(18,21,22,25)(19,23,20,24)(26,29)(27,31)(28,32)(30,33)

Conjugacy classes & character table

572 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15751305, #15751333, #15751397, …
maximal subgroup of	C₁₃×#7666, C₁₃×#7672, C₁₃×#7686, …
maximal normal subgroup of	C₁₃×#7666, C₁₃×#7672, C₁₃×#7686, …
maximal quotient of	C₁₃×#14688, C₁₃×#14699, C₁₃×#14700, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1592);