C₁₃×#3549 #13112607

order	1664
nilpotency class	2
isoclinism	isoclinic class of #3532
automorphism	?
homology	Abelianization (H₁) = C₂⁵×C₁₃ · Schur multiplier (H₂) = C₂⁷×C₄

Aliases

direct product

C₁₃×#3549

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₁₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ G

1258 conjugacy classes of subgroups; only the 768 normal subgroups are shown.

normal subgroups only

This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 768 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 — 5 generators on 29 points:

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

Conjugacy classes & character table

494 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#15755273, #15755474, #15778774, …
maximal subgroup of	C₁₃×#8491, C₁₃×#8530, C₁₃×#12769, …
maximal normal subgroup of	C₁₃×#8491, C₁₃×#8530, C₁₃×#12769, …
maximal quotient of	C₁₃×#34368, C₁₃×#34415, C₁₃×#34485, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1664, 2281);