C₂×C₉×#383 #11767003

order	1152
nilpotency class	2
isoclinism	isoclinic class of #120
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₉ · Schur multiplier (H₂) = C₂⁶

Aliases

direct product

C₂×C₉×#383

Subgroups

	subgroup	G/H
center	C₂⁴×C₉	C₂³
commutator	C₂²	C₂³×C₄×C₉
Frattini, cosocle	C₂³×C₃	C₂⁴×C₃
socle, prime radical	C₂⁴×C₃	C₂³×C₃
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₉ ◁ G

936 conjugacy classes of subgroups; only the 540 normal subgroups are shown.

normal subgroups only

This group has 936 conjugacy classes of subgroups — too many to draw. Only its 540 normal subgroups are shown.

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

Full subgroup data →

Presentation

minimal degree	μ(G) = 31
transitive degree	μ_t(G) = 1152

A minimal faithful permutation representation — 4 generators on 31 points:

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

Conjugacy classes & character table

504 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1152, 1014);