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C22×C29×2−1+4 #16817306

order3712
nilpotency class2
isoclinismisoclinic class of H(5,𝔽2)
automorphism?
homologyAbelianization (H1) = C26×C29 · Schur multiplier (H2) = C214

Aliases

direct productC22×C29×2−1+4

Subgroups

subgroupG/H
center, socleC23×C29C24
commutator, Frattini, cosocleC2C26×C29
LCSG ▷ C2 ▷ C1
UCSC1 ◁ C23×C29 ◁ G

5872 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 49
transitive degreeμt(G) = 1856

A minimal faithful permutation representation — 6 generators on 49 points:

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

Conjugacy classes & character table

1972 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC29×#20587, C29×#20593, C29×#20603, …
maximal normal subgroup ofC29×#20587, C29×#20593, C29×#20603, …
maximal quotient ofC22×C29×#519, C22×C29×#520, C2×C4×C29×2−1+4, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 2324);