Finite Group Databasebeta

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C3×#87658 #11924320

order1176
isoclinismisoclinic class of #87658
automorphism?
homologyAbelianization (H1) = C22×C3 · Schur multiplier (H2) = C7

Aliases

direct productC3×#87658

Splittings

Fitting, socle, HallC3×C72 ⋊ Q8
SylowC72 ⋊ C3×Q8

Subgroups

subgroupG/H
center, hypercenterC3#87658
commutator, cosocleC7⋊D7C22×C3
FrattiniC1G
Fitting, socleC3×C72Q8
prime radicalC3×C7⋊D7C22
hypocenterC72C3×Q8
LCSG ▷ C7⋊D7 ▷ C72
UCSC1 ◁ C3

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 31
transitive degreeμt(G) = 84

A minimal faithful permutation representation — 2 generators on 31 points:

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

Conjugacy classes & character table

33 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 235);