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#66526⋊C2 #10620395

order666
isoclinismisoclinic class of #66526⋊C2
automorphism?
homologyAbelianization (H1) = C2×C9 · Schur multiplier (H2) = C1

Aliases

unambiguous semidirect product#66526⋊C2

Splittings

Fitting, socle, derived, SylowC37 ⋊ C2×C9
Hall#66526 ⋊ C2
HallD37 ⋊ C9

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, hypocenterC37C2×C9
prime radicalD37⋊C3C3
cosocleC37⋊C3C2×C3
LCSG ▷ C37
UCSC1

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37

Polycyclic presentation:

2,3^2,37|b^3=c,d^a=d^36,d^b=d^16,d^c=d^26

Conjugacy classes & character table

20 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofAGL(1,𝔽37), C2×#66526⋊C2, C3×#66526⋊C2, …
maximal normal subgroup ofAGL(1,𝔽37), C2×#66526⋊C2, C3×#66526⋊C2, …
maximal quotient of#13050625, C2×#66526⋊C2, #11758603⋊C2, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(666, 7);