Finite Group Databasebeta

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C22×C5×C13⋊#3862 #50304509

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

Aliases

direct productC22×C5×C13⋊#3862

Splittings

Fitting, socle, HallC22×C5×C72×C13 ⋊ C3
derived, HallC72×C13 ⋊ C22×C3×C5
HallC5×C72×C13 ⋊ C22×C3
HallC22×C72×C13 ⋊ C3×C5
HallC22×C5×C72 ⋊ C13⋊C3
HallC22×C5×C13 ⋊ #3862
HallC5×C72 ⋊ C22×C13⋊C3
HallC22×C72 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ C22×#3862
HallC22×C13 ⋊ C5×#3862
SylowC72 ⋊ C22×C5×C13⋊C3
SylowC13 ⋊ C22×C5×#3862

Subgroups

subgroupG/H
center, hypercenterC22×C5C13⋊#3862
commutator, cosocle, hypocenterC72×C13C22×C3×C5
FrattiniC1G
Fitting, socleC22×C5×C72×C13C3
LCSG ▷ C72×C13
UCSC1 ◁ C22×C5

200 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 200 conjugacy classes of subgroups — too many to draw. Only its 90 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) = 36
transitive degreeμt(G) = 5460

A minimal faithful permutation representation — 2 generators on 36 points:

(1,2)(5,6,7,8,9)(11,12,13)(14,16,15)(18,19,20)(21,23,22)(25,26,28)(27,30,33)(29,32,31)(34,36,35);(3,4)(10,11,12,14,13,15,16)(17,18,20,22,19,21,23)(24,25,27,26,29,33,30,34,36,28,31,35,32)

Conjugacy classes & character table

4300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1195);