C₁₃×#538 #11719573

order	832
nilpotency class	2
isoclinism	isoclinic class of #534
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁴

Aliases

direct product

C₁₃×#538

Subgroups

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

250 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 250 conjugacy classes of subgroups — too many to draw. Only its 146 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)(16,22)(17,21)(18,20)(19,23)(24,26)(25,28)(27,29);(14,16,18,24)(15,19,20,27)(17,23,25,29)(21,22,28,26);(15,20)(16,23)(19,26)(21,28)(22,27)(24,29);(15,21)(19,22)(20,28)(26,27)

Conjugacy classes & character table

286 conjugacy classes — view the full character table.

Relationships

Fitting subgroup of	#13113782, #13113816, #13113850, …
maximal subgroup of	C₁₃×#1600, C₁₃×#1606, C₁₃×#1612, …
maximal normal subgroup of	C₁₃×#1600, C₁₃×#1606, C₁₃×#1612, …
maximal quotient of	C₁₃×#2312, C₁₃×#2318, C₁₃×#2321, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1539);