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C2×C29×#471 #16816778

order3712
nilpotency class3
isoclinismisoclinic class of #471
automorphism?
homologyAbelianization (H1) = C24×C29 · Schur multiplier (H2) = C25

Aliases

direct productC2×C29×#471

Subgroups

subgroupG/H
center, socleC22×C29#121
commutator, Frattini, cosocleC2×C4C24×C29
prime radicalC2×C29×AGL(1,ℤ/8)C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C29 ◁ C22×C4×C29 ◁ G

468 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 47
transitive degreeμt(G) = 928

A minimal faithful permutation representation — 4 generators on 47 points:

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

Conjugacy classes & character table

928 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C29×#471, C29×#21557, C29×#23044, …
maximal normal subgroup ofC4×C29×#471, C29×#21557, C29×#23044, …
maximal quotient ofC2×C29×#1665, C2×C29×#1671, C2×C29×#1681, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1796);