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C22×C29×#107 #16816622

order3712
nilpotency class3
isoclinismisoclinic class of D8
automorphism?
homologyAbelianization (H1) = C23×C4×C29 · Schur multiplier (H2) = C26

Aliases

direct productC22×C29×#107

Subgroups

subgroupG/H
center, socle, prime radicalC24×C29D4
commutatorC4C23×C4×C29
Frattini, cosocleC2×C4C24×C29
LCSG ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C24×C29 ◁ C23×C4×C29 ◁ G

600 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 45
transitive degreeμt(G) = 3712

A minimal faithful permutation representation — 4 generators on 45 points:

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

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC29×#10862, C29×#10863, C29×#10870, …
maximal normal subgroup ofC29×#10862, C29×#10863, C29×#10870, …
maximal quotient ofC22×C29×#335, C2×C29×#1567, C2×C29×#1571, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(3712, 1640);