C₂×C₇×#492 #11742452

order	896
nilpotency class	3
isoclinism	isoclinic class of #465
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

	subgroup	G/H
center, socle	C₂³×C₇	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₇
prime radical	C₂×C₇×#127	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₇ ◁ C₂×C₄²×C₇ ◁ G

656 conjugacy classes of subgroups; only the 264 normal subgroups are shown.

normal subgroups only

This group has 656 conjugacy classes of subgroups — too many to draw. Only its 264 normal subgroups are shown.

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

minimal degree	μ(G) = 21
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 4 generators on 21 points:

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

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 17218);