C₁₃×#14679 #15701018

order	3328
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₁₃ · Schur multiplier (H₂) = C₂¹²

Aliases

direct product

C₁₃×#14679

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₁₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₁₃
Frattini, cosocle	C₂⁴	C₂⁴×C₁₃
prime radical	C₂⁷×C₁₃	C₂
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₁₃ ◁ G

30862 conjugacy classes of subgroups; only the 1374 normal subgroups are shown.

normal subgroups only

This group has 30862 conjugacy classes of subgroups — too many to draw. Only its 1374 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) = 416

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

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

Conjugacy classes & character table

1144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3328, 7667);