C₇×#447 #90093

order	448
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂³×C₇ · Schur multiplier (H₂) = C₂⁴

Aliases

	subgroup	G/H
center, socle	C₂²×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂³×C₇
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₇ ◁ C₂²×C₄×C₇ ◁ G

198 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 198 conjugacy classes of subgroups — too many to draw. Only its 62 normal subgroups are shown.

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

minimal degree	μ(G) = 19
transitive degree	μ_t(G) = 112

A minimal faithful permutation representation — 3 generators on 19 points:

(1,2)(3,4)(5,6)(7,9)(8,11)(10,12)(13,14,15,16,17,18,19);(6,9)(7,12)(10,11);(2,4)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(448, 855);