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C5×#18011724 #37558191

order23790
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#18011724

Splittings

Fitting, socle, HallC5×C13×C61 ⋊ C2×C3
derived, HallC13×C61 ⋊ C2×C3×C5
HallC5×#14558651 ⋊ C2
HallC5×C13×D61 ⋊ C3
Hall#14558651 ⋊ C2×C5
HallC13×D61 ⋊ C3×C5
HallC5×D61 ⋊ C13⋊C3
HallC5×C61 ⋊ C2×C13⋊C3
HallD61 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ D61⋊C3
SylowC61 ⋊ C2×C5×C13⋊C3
SylowC13 ⋊ C5×D61⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#18011724
commutator, cosocle, hypocenterC13×C61C2×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C61C2×C3
LCSG ▷ C13×C61
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3965

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(23790, 36);