Finite Group Databasebeta

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C32×#92788 #72228858

order4563
isoclinismisoclinic class of #92788
automorphism?
homologyAbelianization (H1) = C33 · Schur multiplier (H2) = C33

Aliases

direct productC32×#92788

Splittings

Fitting, socleC32×C132 ⋊ C3
derived, SylowC132 ⋊ C33

Subgroups

subgroupG/H
center, hypercenterC32#92788
commutator, cosocle, hypocenterC132C33
FrattiniC1G
Fitting, socleC32×C132C3
LCSG ▷ C132
UCSC1 ◁ C32

448 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1521

A minimal faithful permutation representation — 3 generators on 32 points:

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

Conjugacy classes & character table

531 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup of#72228894, C32×#11759815
maximal normal subgroup of#72228894, C32×#11759815

GAP

Past the SmallGroups library coverage — no SmallGroups id. Construct it from a minimal faithful permutation representation:

gap> G := Group((14,15,17,18,21,20,24,26,25,16,19,23,22)(30,31,32), (2,3,5)(4,7,11)(6,9,8)(10,12,13)(15,16,18)(17,20,24)(19,22,21)(23,25,26), (1,2,4,5,8,7,11,13,12,3,6,10,9)(27,28,29));