Finite Group Databasebeta

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D3×C23×D37⋊C3 #44499673

order30636
automorphism?
homologyAbelianization (H1) = C22×C3×C23 · Schur multiplier (H2) = C2

Aliases

direct productD3×C23×D37⋊C3
unambiguous semidirect productD37⋊(C3×D3×C23)
unambiguous semidirect product(D3×D37)⋊(C3×C23)
unambiguous semidirect product(C3×D37⋊C3)⋊(C2×C23)
unambiguous semidirect product(D3×C37⋊C3)⋊(C2×C23)
unambiguous semidirect product(C3⋊(D37⋊C3))⋊(C2×C23)
unambiguous semidirect product(D3×C23×D37)⋊C3

Splittings

Fitting, socleC3×C23×C37 ⋊ C22×C3
derivedC3×C37 ⋊ C22×C3×C23
HallC3×C23×C37⋊C3 ⋊ C22
HallC23×C37 ⋊ C2×C3×D3
HallC3×C37⋊C3 ⋊ C22×C23
SylowC37 ⋊ C2×C3×D3×C23

Subgroups

subgroupG/H
center, hypercenterC23D3×D37⋊C3
commutator, cosocle, hypocenterC3×C37C22×C3×C23
FrattiniC1G
Fitting, socleC3×C23×C37C22×C3
LCSG ▷ C3×C37
UCSC1 ◁ C23

88 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2553

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30636, 76);