C₁₃×#12778 #15699117

order	3328
nilpotency class	4
isoclinism	isoclinic class of #12778
automorphism	?
homology	Abelianization (H₁) = C₂²×C₄×C₁₃ · Schur multiplier (H₂) = C₂⁴×C₄

Aliases

direct product

C₁₃×#12778

Subgroups

	subgroup	G/H
center, socle	C₂×C₁₃	#1790
commutator	C₂×Q₈	C₂²×C₄×C₁₃
Frattini, cosocle	C₂×#41	C₂³×C₁₃
prime radical	C₁₃×#3549	C₂
LCS	G ▷ C₂×Q₈ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₁₃ ◁ C₂×C₄×C₁₃ ◁ C₂×C₁₃×#41 ◁ G

860 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 860 conjugacy classes of subgroups — too many to draw. Only its 138 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) = 29
transitive degree	μ_t(G) = 208

A minimal faithful permutation representation — 3 generators on 29 points:

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

Conjugacy classes & character table

442 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 5766);