C₁₃×#2823 #13111881

order	1664
nilpotency class	2
isoclinism	isoclinic class of #2812
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#2823

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

456 conjugacy classes of subgroups; only the 184 normal subgroups are shown.

normal subgroups only

This group has 456 conjugacy classes of subgroups — too many to draw. Only its 184 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)(18,19,21,23)(20,22,24,25)(26,27,30,31)(28,29,32,33);(15,17)(20,24)(22,25)(27,31)(29,33);(14,15)(16,17)(18,19)(20,22)(21,23)(24,25)(26,28)(27,29)(30,32)(31,33);(18,20,21,24)(19,22,23,25)(26,29)(27,32)(28,31)(30,33)

Conjugacy classes & character table

338 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15775344, #15775930, D₁₃×#2823, …
maximal subgroup of	C₁₃×#12155, C₁₃×#12249, C₂×C₁₃×#2823, …
maximal normal subgroup of	C₁₃×#12155, C₁₃×#12249, C₂×C₁₃×#2823, …
maximal quotient of	C₁₃×#14632, C₁₃×#14633, C₁₃×#14634, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1555);