C₂×C₂₉×#390 #16816006

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂³×C₄×C₂₉ · Schur multiplier (H₂) = C₂⁶×C₄

Aliases

direct product

C₂×C₂₉×#390

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₂₉	C₂³
commutator	C₂²	C₂³×C₄×C₂₉
Frattini, cosocle	C₂³	C₂⁴×C₂₉
prime radical	C₂³×D₄×C₂₉	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

1360 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 43
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 43 points:

(1,2)(15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43);(4,6)(8,9)(11,12,14,13);(7,8,10,9)(11,13,14,12);(3,4,5,6)(7,9,10,8)

Conjugacy classes & character table

1624 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of	C₂×C₂₉×#1270, C₂₉×#7572, C₂₉×#7592, …
maximal normal subgroup of	C₂×C₂₉×#1270, C₂₉×#7572, C₂₉×#7592, …
maximal quotient of	C₂×C₂₉×C₄⋊#95, C₂×C₂₉×#1437, C₄×C₂₉×#390, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1024);

C2×C29×#390 #16816006