Finite Group Databasebeta

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C2×C5×C13⋊#64418 #50304218

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

Aliases

direct productC2×C5×C13⋊#64418
unambiguous semidirect product(C2×C13)⋊(C5×#64418)

Splittings

Fitting, socleC2×C5×C72×C13 ⋊ D3
derived, HallC13×#3862 ⋊ C22×C5
HallC5×C13×#3862 ⋊ C22
HallC5×C72×C13 ⋊ C2×D3
HallC5×#3862 ⋊ C2×D13
HallC72×C13 ⋊ C2×C5×D3
HallC5×C72 ⋊ C2×D39
Hall#3862 ⋊ C2×C5×D13
HallC5×C13 ⋊ C2×#64418
SylowC72 ⋊ C2×C5×D39
SylowC13 ⋊ C2×C5×#64418

Subgroups

subgroupG/H
center, hypercenterC2×C5C13⋊#64418
commutator, cosocle, hypocenterC13×#3862C22×C5
FrattiniC1G
Fitting, socleC2×C5×C72×C13D3
LCSG ▷ C13×#3862
UCSC1 ◁ C2×C5

136 conjugacy classes of subgroups; only the 30 normal subgroups are shown.

normal subgroups only

This group has 136 conjugacy classes of subgroups — too many to draw. Only its 30 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) = 34
transitive degreeμt(G) = 1820

A minimal faithful permutation representation — 2 generators on 34 points:

(3,4,5,6,7)(8,11,21,18,17,13,15,16,20,9,10,19,14,12)(23,24)(25,26)(27,28)(29,30)(31,32)(33,34);(1,2)(10,14,15)(11,16,13)(12,18,19)(17,21,20)(22,23,25,27,29,31,33,34,32,30,28,26,24)

Conjugacy classes & character table

1340 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 904);