Finite Group Databasebeta

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C5×#14558780⋊C2 #37560918

order23940
automorphism?
homologyAbelianization (H1) = C22×C5×C9 · Schur multiplier (H2) = C2

Aliases

direct productC5×#14558780⋊C2
unambiguous semidirect product#14558780⋊(C2×C5)
unambiguous semidirect product#14558784⋊(C2×C5)
unambiguous semidirect product#14558786⋊(C2×C5)

Splittings

derived, HallC7×C19 ⋊ C22×C5×C9
HallC5×#11924776 ⋊ C22
HallC5×D7×D19 ⋊ C9
Hall#11924776 ⋊ C22×C5
HallC5×C7×C19 ⋊ C22×C9
HallD7×D19 ⋊ C5×C9
HallC5×C19 ⋊ C2×D7⋊C9
HallC5×C7 ⋊ C2×#4294⋊C2
SylowC19 ⋊ C2×C5×D7⋊C9
SylowC7 ⋊ C2×C5×#4294⋊C2

Subgroups

subgroupG/H
center, hypercenterC3×C5#11716321⋊C2
commutator, hypocenterC7×C19C22×C5×C9
FrattiniC3C5×#11716321⋊C2
Fitting, socleC3×C5×C7×C19C22×C3
prime radicalC3×C5×D7×D19C3
cosocleC3×C7×C19C22×C3×C5
LCSG ▷ C7×C19
UCSC1 ◁ C3×C5

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

normal subgroups only

This group has 120 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) = 5985

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23940, 50);