Finite Group Databasebeta

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C2×C7×D1365 #50304530

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

Aliases

direct productC2×C7×D1365
unambiguous semidirect product(C2×C3)⋊(C7×D455)
unambiguous semidirect product(C2×C5)⋊(C7×D273)
unambiguous semidirect product(C2×C7)⋊(C7×D195)
unambiguous semidirect product(C2×C13)⋊(C7×D105)

Splittings

Fitting, socleC2×C3×C5×C72×C13 ⋊ C2
derivedC3×C5×C7×C13 ⋊ C22×C7
HallC3×C5×C72×C13 ⋊ C22
HallC5×C72×C13 ⋊ C2×D3
HallC3×C72×C13 ⋊ C2×D5
HallC3×C5×C72 ⋊ C2×D13
HallC72×C13 ⋊ C2×D15
HallC5×C72 ⋊ C2×D39
HallC3×C5×C13 ⋊ C2×C7×D7
HallC3×C72 ⋊ C2×D65
HallC5×C13 ⋊ C2×C7×D21
SylowC72 ⋊ C2×D195
HallC3×C13 ⋊ C2×C7×D35
HallC3×C5 ⋊ C2×C7×D91
SylowC13 ⋊ C2×C7×D105
SylowC5 ⋊ C2×C7×D273
SylowC3 ⋊ C2×C7×D455

Subgroups

subgroupG/H
center, hypercenterC2×C7D1365
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C7
FrattiniC1G
Fitting, socleC2×C3×C5×C72×C13C2
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C2×C7

208 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 70 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) = 5460

Conjugacy classes & character table

9576 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(38220, 1216);