C₂×C₂₉×#433 #16816633

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

Aliases

direct product

C₂×C₂₉×#433

Subgroups

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

412 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degree	μ(G) = 55
transitive degree	μ_t(G) = 1856

A minimal faithful permutation representation — 4 generators on 55 points:

(1,2)(27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55);(3,4)(5,8)(6,7)(9,10)(11,12,14,17,15,18,21,24)(13,16,20,23,19,22,25,26);(4,7)(8,10)(11,13)(12,16)(14,20)(15,19)(17,23)(18,22)(21,25)(24,26);(3,5,6,9)(4,8,7,10)(13,19)(16,22)(20,25)(23,26)

Conjugacy classes & character table

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

Relationships

maximal subgroup of	C₂₉×#8158, C₂₉×#8603, C₂₉×#11461, …
maximal normal subgroup of	C₂₉×#8158, C₂₉×#8603, C₂₉×#11461, …
maximal quotient of	C₂×C₂₉×#1746, C₂×C₂₉×#1750, C₂×C₂₉×#1768, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1651);

C2×C29×#433 #16816633