Finite Group Databasebeta

← Prev (#11924313) Next (#11924315) →

C3×#87656 #11924314

order1176
isoclinismisoclinic class of #87656
automorphism?
homologyAbelianization (H1) = C3×C8 · Schur multiplier (H2) = C7

Aliases

direct productC3×#87656

Splittings

Fitting, socle, HallC3×C72 ⋊ C8
derived, SylowC72 ⋊ C3×C8

Subgroups

subgroupG/H
center, hypercenterC3#87656
commutator, hypocenterC72C3×C8
FrattiniC1G
Fitting, socleC3×C72C8
prime radicalC3×C7⋊D7C4
cosocle#5997C2×C3
LCSG ▷ C72
UCSC1 ◁ C3

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

Conjugacy classes & character table

42 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1176, 229);