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C17×D15×C37 #34038273

order18870
automorphism?
homologyAbelianization (H1) = C2×C17×C37 · Schur multiplier (H2) = C1

Aliases

direct productC17×D15×C37
unambiguous semidirect productC3⋊(D5×C17×C37)
unambiguous semidirect productC5⋊(D3×C17×C37)

Splittings

Fitting, socle, HallC3×C5×C17×C37 ⋊ C2
derived, HallC3×C5 ⋊ C2×C17×C37
HallC5×C17×C37 ⋊ D3
HallC3×C17×C37 ⋊ D5
HallC3×C5×C37 ⋊ C2×C17
HallC3×C5×C17 ⋊ C2×C37
HallC5×C37 ⋊ D3×C17
HallC3×C37 ⋊ D5×C17
HallC5×C17 ⋊ D3×C37
HallC3×C17 ⋊ D5×C37
SylowC5 ⋊ D3×C17×C37
SylowC3 ⋊ D5×C17×C37

Subgroups

subgroupG/H
center, hypercenterC17×C37D15
commutator, cosocle, hypocenterC3×C5C2×C17×C37
FrattiniC1G
Fitting, socleC3×C5×C17×C37C2
LCSG ▷ C3×C5
UCSC1 ◁ C17×C37

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9435

Conjugacy classes & character table

5661 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC17×D15×D37, D15×D17×C37, D15×D629, …
maximal normal subgroup ofC17×D15×D37, D15×D17×C37, D15×D629, …
maximal quotient ofC17×C37×Dic15, C2×C17×D15×C37

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18870, 14);