Finite Group Databasebeta

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C3×C5×D11×D37 #37567573

order24420
automorphism?
homologyAbelianization (H1) = C22×C3×C5 · Schur multiplier (H2) = C2

Aliases

direct productC3×C5×D11×D37

Splittings

Fitting, socle, HallC3×C5×C11×C37 ⋊ C22
derived, HallC11×C37 ⋊ C22×C3×C5
HallC5×C11×C37 ⋊ C22×C3
HallC3×C11×C37 ⋊ C22×C5
HallC3×C5×C37 ⋊ C2×D11
HallC5×C37 ⋊ C2×C3×D11
HallC3×C5×C11 ⋊ C2×D37
HallC3×C37 ⋊ C2×C5×D11
HallC5×C11 ⋊ C2×C3×D37
SylowC37 ⋊ C2×C3×C5×D11
HallC3×C11 ⋊ C2×C5×D37
SylowC11 ⋊ C2×C3×C5×D37

Subgroups

subgroupG/H
center, hypercenterC3×C5D11×D37
commutator, cosocle, hypocenterC11×C37C22×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C11×C37C22
LCSG ▷ C11×C37
UCSC1 ◁ C3×C5

80 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6105

Conjugacy classes & character table

2100 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(24420, 94);