Finite Group Databasebeta

← Prev (#49178761) Next (#49178763) →

C3⋊D3×D1045 #49178762

order37620
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2×C3

Aliases

direct productC3⋊D3×D1045

Splittings

Fitting, socle, derived, HallC32×C5×C11×C19 ⋊ C22
HallC32×C11×C19 ⋊ C2×D5
HallC5×C11×C19 ⋊ C2×C3⋊D3
HallC32×C5×C19 ⋊ C2×D11
HallC32×C5×C11 ⋊ C2×D19
HallC11×C19 ⋊ D5×C3⋊D3
HallC32×C19 ⋊ C2×D55
HallC32×C11 ⋊ C2×D95
HallC5×C19 ⋊ C3⋊D3×D11
HallC5×C11 ⋊ C3⋊D3×D19
HallC32×C5 ⋊ C2×D209
SylowC19 ⋊ C3⋊D3×D55
SylowC11 ⋊ C3⋊D3×D95
SylowC32 ⋊ C2×D1045
SylowC5 ⋊ C3⋊D3×D209

Subgroups

subgroupG/H
center, Frattini, hypercenterC1G
commutator, Fitting, socle, cosocle, hypocenterC32×C5×C11×C19C22
LCSG ▷ C32×C5×C11×C19
UCSC1

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

normal subgroups only

This group has 240 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) = 9405

Conjugacy classes & character table

3144 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37620, 471);