C₃²×D₄² #10596346

order	576
nilpotency class	2
isoclinism	isoclinic class of D₄²
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₃² · Schur multiplier (H₂) = C₂⁶×C₃

Aliases

C₃²×D₄²

	subgroup	G/H
center, socle	C₂²×C₃²	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁴×C₃²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃² ◁ G

1284 conjugacy classes of subgroups; only the 546 normal subgroups are shown.

normal subgroups only

This group has 1284 conjugacy classes of subgroups — too many to draw. Only its 546 normal subgroups are shown.

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

minimal degree	μ(G) = 14
transitive degree	μ_t(G) = 144

A minimal faithful permutation representation — 4 generators on 14 points:

(1,2,3)(7,8,9,10);(4,5,6)(8,10);(11,12,13,14);(12,14)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(576, 8228);