Finite Group Databasebeta

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C5×D13×D105 #41031972

order27300
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2

Aliases

direct productC5×D13×D105
unambiguous semidirect product(C3×D13)⋊(C5×D35)
unambiguous semidirect product(C5×D13)⋊(C5×D21)
unambiguous semidirect product(C7×D13)⋊(C5×D15)

Splittings

Fitting, socle, HallC3×C52×C7×C13 ⋊ C22
derivedC3×C5×C7×C13 ⋊ C22×C5
HallC52×C7×C13 ⋊ C2×D3
HallC3×C52×C13 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D13
HallC52×C13 ⋊ C2×D21
HallC3×C7×C13 ⋊ C2×C5×D5
HallC52×C7 ⋊ D3×D13
HallC7×C13 ⋊ C2×C5×D15
HallC3×C52 ⋊ D7×D13
HallC3×C13 ⋊ C2×C5×D35
SylowC52 ⋊ D13×D21
HallC3×C7 ⋊ C5×D5×D13
SylowC13 ⋊ C2×C5×D105
SylowC7 ⋊ C5×D13×D15
SylowC3 ⋊ C5×D13×D35

Subgroups

subgroupG/H
center, hypercenterC5D13×D105
commutator, cosocle, hypocenterC3×C5×C7×C13C22×C5
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C3×C5×C7×C13
UCSC1 ◁ C5

192 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 56 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

2160 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 862);