Finite Group Databasebeta

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C3×C5×D13×D35 #41031908

order27300
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C5×D13×D35

Splittings

Fitting, socle, HallC3×C52×C7×C13 ⋊ C22
derivedC5×C7×C13 ⋊ C22×C3×C5
HallC52×C7×C13 ⋊ C22×C3
HallC3×C52×C13 ⋊ C2×D7
HallC3×C52×C7 ⋊ C2×D13
HallC52×C13 ⋊ C2×C3×D7
HallC3×C7×C13 ⋊ C2×C5×D5
HallC52×C7 ⋊ C2×C3×D13
HallC7×C13 ⋊ C2×C3×C5×D5
HallC3×C52 ⋊ D7×D13
HallC3×C13 ⋊ C2×C5×D35
SylowC52 ⋊ C3×D7×D13
HallC3×C7 ⋊ C5×D5×D13
SylowC13 ⋊ C2×C3×C5×D35
SylowC7 ⋊ C3×C5×D5×D13

Subgroups

subgroupG/H
center, hypercenterC3×C5D13×D35
commutator, cosocle, hypocenterC5×C7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC3×C52×C7×C13C22
LCSG ▷ C5×C7×C13
UCSC1 ◁ C3×C5

192 conjugacy classes of subgroups; only the 64 normal subgroups are shown.

normal subgroups only

This group has 192 conjugacy classes of subgroups — too many to draw. Only its 64 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

2280 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 798);