Finite Group Databasebeta

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C3×C5×D629 #34038264

order18870
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×D629
unambiguous semidirect productC17⋊(C3×C5×D37)

Splittings

Fitting, socle, HallC3×C5×C17×C37 ⋊ C2
derived, HallC17×C37 ⋊ C2×C3×C5
HallC5×C17×C37 ⋊ C2×C3
HallC3×C17×C37 ⋊ C2×C5
HallC3×C5×C37 ⋊ D17
HallC3×C5×C17 ⋊ D37
HallC5×C37 ⋊ C3×D17
HallC3×C37 ⋊ C5×D17
HallC5×C17 ⋊ C3×D37
HallC3×C17 ⋊ C5×D37
SylowC37 ⋊ C3×C5×D17
SylowC17 ⋊ C3×C5×D37

Subgroups

subgroupG/H
center, hypercenterC3×C5D629
commutator, cosocle, hypocenterC17×C37C2×C3×C5
FrattiniC1G
Fitting, socleC3×C5×C17×C37C2
LCSG ▷ C17×C37
UCSC1 ◁ C3×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9435

Conjugacy classes & character table

4740 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×#14578979, C3×C5×#14578980, C3×C5×D17×D37, …
maximal normal subgroup ofC3×C5×#14578979, C3×C5×#14578980, C3×C5×D17×D37, …
maximal quotient ofC3×C5×Dic629, C2×C3×C5×D629

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18870, 5);