Finite Group Databasebeta

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C13×#15668837 #50304442

order38220
automorphism?
homologyAbelianization (H1) = C22×C13 · Schur multiplier (H2) = C2

Aliases

direct productC13×#15668837

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C22
derived, HallC3×C5×C72 ⋊ C22×C13
HallC5×C72×C13 ⋊ C2×D3
HallC3×C72×C13 ⋊ C2×D5
HallC72×C13 ⋊ C2×D15
HallC5×C72 ⋊ C2×D3×C13
HallC3×C5×C13 ⋊ D72
HallC3×C72 ⋊ C2×D5×C13
HallC5×C13 ⋊ D21⋊D7
SylowC72 ⋊ C2×C13×D15
HallC3×C13 ⋊ D35⋊D7
HallC3×C5 ⋊ C13×D72
SylowC5 ⋊ C13×D21⋊D7
SylowC3 ⋊ C13×D35⋊D7

Subgroups

subgroupG/H
center, hypercenterC13#15668837
commutator, cosocle, hypocenterC3×C5×C72C22×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C22
LCSG ▷ C3×C5×C72
UCSC1 ◁ C13

208 conjugacy classes of subgroups; only the 50 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 50 normal subgroups are shown.

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

Full subgroup data →

Presentation

transitive degreeμt(G) = 2730

Conjugacy classes & character table

2691 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1128);