Finite Group Databasebeta

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C5×(C5⋊(D13⋊C3))⋊D7 #41031625

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

Aliases

direct productC5×(C5⋊(D13⋊C3))⋊D7
unambiguous semidirect product(C5⋊(D13⋊C3))⋊(C5×D7)
unambiguous semidirect product((C13⋊C3)⋊D7)⋊(C5×D5)

Splittings

Fitting, socle, HallC52×C7×C13 ⋊ C22×C3
derivedC5×C7×C13 ⋊ C22×C3×C5
HallC5×D35⋊D13 ⋊ C3
HallC52×C7×C13⋊C3 ⋊ C22
HallC52×C13⋊C3 ⋊ C2×D7
HallC52×C13 ⋊ C2×C3×D7
HallC7×C13⋊C3 ⋊ C2×C5×D5
HallC52×C7 ⋊ C2×D13⋊C3
HallC7×C13 ⋊ C2×C3×C5×D5
HallC13⋊C3 ⋊ C5×D5×D7
SylowC52 ⋊ D7×D13⋊C3
SylowC13 ⋊ C3×C5×D5×D7
SylowC7 ⋊ C5×D5×D13⋊C3

Subgroups

subgroupG/H
center, hypercenterC5(C5⋊(D13⋊C3))⋊D7
commutator, cosocle, hypocenterC5×C7×C13C22×C3×C5
FrattiniC1G
Fitting, socleC52×C7×C13C22×C3
LCSG ▷ C5×C7×C13
UCSC1 ◁ C5

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

normal subgroups only

This group has 192 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) = 910

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27300, 515);