Finite Group Databasebeta

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C5×D13×#64425 #50303805

order38220
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productC5×D13×#64425

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C22×C3
derived, HallC72×C13 ⋊ C22×C3×C5
HallC5×D13×C7⋊D7 ⋊ C3
HallC5×C13×#3862 ⋊ C22
HallD13×C7⋊D7 ⋊ C3×C5
HallC13×#3862 ⋊ C22×C5
HallC5×#3862 ⋊ C2×D13
HallC5×C72 ⋊ C2×C3×D13
Hall#3862 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×#64425
SylowC72 ⋊ C2×C3×C5×D13
SylowC13 ⋊ C2×C5×#64425

Subgroups

subgroupG/H
center, hypercenterC5D13×#64425
commutator, cosocle, hypocenterC72×C13C22×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C13C22×C3
LCSG ▷ C72×C13
UCSC1 ◁ C5

200 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 46 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

minimal degreeμ(G) = 32
transitive degreeμt(G) = 1365

A minimal faithful permutation representation — 2 generators on 32 points:

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

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 491);