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C2×#66526 #10620396

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

Aliases

direct productC2×#66526

Splittings

Fitting, socle, HallC2×C37 ⋊ C9
derived, SylowC37 ⋊ C2×C9

Subgroups

subgroupG/H
center, hypercenterC2#66526
commutator, hypocenterC37C2×C9
FrattiniC1G
Fitting, socleC2×C37C9
prime radicalC2×C37⋊C3C3
cosocleC37⋊C3C2×C3
LCSG ▷ C37
UCSC1 ◁ C2

12 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 39
transitive degreeμt(G) = 74

A minimal faithful permutation representation — 2 generators on 39 points:

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

Conjugacy classes & character table

26 conjugacy classes — view the full character table.

Relationships

maximal subgroup of#13050625, C4×#66526, C2×#66526⋊C2, …
maximal normal subgroup of#13050625, C4×#66526, C2×#66526⋊C2, …
maximal quotient ofC4×#66526, C22×#66526, C2×#11758603, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(666, 8);