C₁₃×#548 #11719583

order	832
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₁₃ · Schur multiplier (H₂) = C₂⁵

Aliases

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

290 conjugacy classes of subgroups; only the 166 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

minimal degree	μ(G) = 25
transitive degree	μ_t(G) = 416

A minimal faithful permutation representation — 4 generators on 25 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(832, 1549);