C₂×C₂₃×#121 #13092071

order	1472
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂⁴×C₂₃ · Schur multiplier (H₂) = C₂⁶

Aliases

C₂×C₂₃×#121

	subgroup	G/H
center, socle	C₂³×C₂₃	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁴×C₂₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₂₃ ◁ G

426 conjugacy classes of subgroups; only the 194 normal subgroups are shown.

normal subgroups only

This group has 426 conjugacy classes of subgroups — too many to draw. Only its 194 normal subgroups are shown.

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

minimal degree	μ(G) = 33
transitive degree	μ_t(G) = 736

A minimal faithful permutation representation — 4 generators on 33 points:

(1,2)(11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33);(4,6)(8,10);(7,8,9,10);(3,4)(5,6)

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1472, 203);