C₂₉×C₂²⋊#95 #16815147

order	3712
nilpotency class	2
automorphism	?
homology	Abelianization (H₁) = C₂×C₄²×C₂₉ · Schur multiplier (H₂) = C₂⁷

Aliases

direct product	C₂₉×C₂²⋊#95
unambiguous semidirect product	C₂²⋊(C₂₉×#95)

Subgroups

	subgroup	G/H
center, socle	C₂⁴×C₂₉	C₂³
commutator	C₂²	C₂×C₄²×C₂₉
Frattini, cosocle	C₂⁴	C₂³×C₂₉
prime radical	C₂⁵×C₂₉	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁴×C₂₉ ◁ G

1088 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 45
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 3 generators on 45 points:

(1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29)(31,33)(34,35,36,37)(39,41);(38,39)(40,41)(42,43,44,45);(30,31)(32,33)(34,35)(36,37)(38,39)(40,41)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#7032, C₂₉×#7035, C₂₉×#7187, …
maximal normal subgroup of	C₂₉×#7032, C₂₉×#7035, C₂₉×#7187, …
maximal quotient of	C₂₉×#7554, C₂₉×#7555, C₂₉×#7557, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 165);

C29×C22⋊#95 #16815147