Finite Group Databasebeta

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C3×C5×Dic3×C37 #20269072

order6660
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic3×C37
unambiguous semidirect productC3⋊(C3×C4×C5×C37)

Splittings

derivedC3 ⋊ C3×C4×C5×C37
HallC32×C5×C37 ⋊ C4
HallC32×C37 ⋊ C4×C5
HallC32×C5 ⋊ C4×C37
SylowC32 ⋊ C4×C5×C37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C37D3
commutator, hypocenterC3C3×C4×C5×C37
FrattiniC2C3×C5×D3×C37
Fitting, socleC2×C32×C5×C37C2
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C37

56 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3330 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×Dic3×C25×C37, C3×C5×C37×Dic15, C3×C52×Dic3×C37, …
maximal normal subgroup ofC3×Dic3×C25×C37, C3×C52×Dic3×C37
maximal quotient ofC3×Dic3×C25×C37, C3×C5×C37×Dic15, C3×C52×Dic3×C37, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(6660, 69);