C₂×C₇×#451 #11742308

order	896
nilpotency class	3
isoclinism	isoclinic class of #447
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₇ · Schur multiplier (H₂) = C₂⁶

Aliases

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

740 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 740 conjugacy classes of subgroups — too many to draw. Only its 248 normal subgroups are shown.

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

minimal degree	μ(G) = 29
transitive degree	μ_t(G) = 448

A minimal faithful permutation representation — 4 generators on 29 points:

(1,2)(23,24,25,26,27,28,29);(3,4)(5,6)(7,8,11,14)(9,15,17,22)(10,18,20,13)(12,19,21,16);(7,9,11,17)(8,12,14,21)(10,19,20,16)(13,22,18,15);(4,6)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(896, 17074);