C₁₃×#482 #11719017

order	832
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₁₃ · Schur multiplier (H₂) = C₄

Aliases

direct product

C₁₃×#482

Subgroups

	subgroup	G/H
center, socle	C₂²×C₁₃	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₁₃
prime radical	C₁₃×#121	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₁₃ ◁ C₂²×C₄×C₁₃ ◁ G

106 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 50 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 — 3 generators on 29 points:

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

Conjugacy classes & character table

247 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	D₁₃×#482, #13124748, #13124764, …
maximal subgroup of	C₂×C₁₃×#482, C₁₃×#3091, C₁₃×#3093, …
maximal normal subgroup of	C₂×C₁₃×#482, C₁₃×#3091, C₁₃×#3093, …
maximal quotient of	C₁₃×#1825, C₁₃×#1854, C₁₃×#1875, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 983);