Finite Group Databasebeta

← Prev (#37564006) Next (#37564008) →

C2×C5×C13×D93 #37564007

order24180
automorphism?
homologyAbelianization (H1) = C22×C5×C13 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C13×D93
unambiguous semidirect product(C2×C3)⋊(C5×C13×D31)

Splittings

Fitting, socleC2×C3×C5×C13×C31 ⋊ C2
derived, HallC3×C31 ⋊ C22×C5×C13
HallC3×C5×C13×C31 ⋊ C22
HallC5×C13×C31 ⋊ C2×D3
HallC3×C13×C31 ⋊ C22×C5
HallC3×C5×C31 ⋊ C22×C13
HallC13×C31 ⋊ C2×C5×D3
HallC3×C5×C13 ⋊ C2×D31
HallC5×C31 ⋊ C2×D3×C13
HallC3×C13 ⋊ C2×C5×D31
SylowC31 ⋊ C2×C5×D3×C13
HallC3×C5 ⋊ C2×C13×D31
SylowC3 ⋊ C2×C5×C13×D31

Subgroups

subgroupG/H
center, hypercenterC2×C5×C13D93
commutator, cosocle, hypocenterC3×C31C22×C5×C13
FrattiniC1G
Fitting, socleC2×C3×C5×C13×C31C2
LCSG ▷ C3×C31
UCSC1 ◁ C2×C5×C13

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 12090

Conjugacy classes & character table

6240 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24180, 306);