Finite Group Databasebeta

← Prev (#11759252) Next (#11759254) →

C32×#1144 #11759253

order1008
isoclinismisoclinic class of #1141
automorphism?
homologyAbelianization (H1) = C22×C32 · Schur multiplier (H2) = C3

Aliases

direct productC32×#1144

Splittings

HallC32×C7 ⋊ Q16
SylowC7 ⋊ C32×Q16

Subgroups

subgroupG/H
centerC2×C32C22⋊D7
commutator, cosocleC4×C7C22×C32
FrattiniC4C2×C32×D7
FittingC32×C7×Q8C2
socle, prime radicalC2×C32×C7D4
hypercenterC32×Q8D7
hypocenterC7C32×Q16
LCSG ▷ C4×C7 ▷ C2×C7 ▷ C7
UCSC1 ◁ C2×C32 ◁ C32×C4 ◁ C32×Q8

108 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 29
transitive degreeμt(G) = 1008

A minimal faithful permutation representation — 2 generators on 29 points:

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

Conjugacy classes & character table

198 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1008, 424);