C₁₃×#577 #11719612

order	832
nilpotency class	3
isoclinism	isoclinic class of #576
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

direct product

C₁₃×#577

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	C₂²×D₄
commutator, Frattini, cosocle	C₄	C₂⁴×C₁₃
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₁₃×#41 ◁ G

258 conjugacy classes of subgroups; only the 158 normal subgroups are shown.

normal subgroups only

This group has 258 conjugacy classes of subgroups — too many to draw. Only its 158 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) = 208

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

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

Conjugacy classes & character table

286 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#13126598, #13126609, #13126616, …
maximal subgroup of	C₁₃×#3288, C₁₃×#3289, C₁₃×#3290, …
maximal normal subgroup of	C₁₃×#3288, C₁₃×#3289, C₁₃×#3290, …
maximal quotient of	C₁₃×#2897, C₁₃×#2898, C₁₃×#2912, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1578);