C₁₃×#3192 #13112250

order	1664
nilpotency class	3
isoclinism	isoclinic class of #3192
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂³×C₄

Aliases

direct product

C₁₃×#3192

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₁₃
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂³×C₄×C₁₃ ◁ G

514 conjugacy classes of subgroups; only the 176 normal subgroups are shown.

normal subgroups only

This group has 514 conjugacy classes of subgroups — too many to draw. Only its 176 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) = 29
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 4 generators on 29 points:

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

Conjugacy classes & character table

338 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15759956, #15763225, #15763239, …
maximal subgroup of	C₁₃×#9343, C₁₃×#9930, C₁₃×#9932, …
maximal normal subgroup of	C₁₃×#9343, C₁₃×#9930, C₁₃×#9932, …
maximal quotient of	C₁₃×#21764, C₁₃×#21942, C₁₃×#22046, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 1924);