Finite Group Databasebeta

← Prev (#13132332) Next (#13132334) →

C5×#66633 #13132333

order1680
isoclinismisoclinic class of #66632
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#66633

Splittings

HallC3×C5×C7 ⋊ SD16
HallC5×C7 ⋊ #214
HallC3×C7 ⋊ C5×SD16
HallC3×C5 ⋊ #1142
SylowC7 ⋊ C5×#214
SylowC3 ⋊ C5×#1142

Subgroups

subgroupG/H
centerC2×C5#4268
commutator, cosocleC3×C4×C7C22×C5
FrattiniC4C2×C5×D21
Fitting, prime radicalC3×C5×C7×D4C2
socleC2×C3×C5×C7D4
hypercenterC5×D4D21
hypocenterC3×C7C5×SD16
LCSG ▷ C3×C4×C7 ▷ C2×C3×C7 ▷ C3×C7
UCSC1 ◁ C2×C5 ◁ C4×C5 ◁ C5×D4

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

minimal degreeμ(G) = 23
transitive degreeμt(G) = 840

A minimal faithful permutation representation — 2 generators on 23 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1680, 353);