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C5×C17×D111 #34038270

order18870
automorphism?
homologyAbelianization (H1) = C2×C5×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C17×D111
unambiguous semidirect productC3⋊(C5×C17×D37)
unambiguous semidirect productC37⋊(C5×D3×C17)

Splittings

Fitting, socle, HallC3×C5×C17×C37 ⋊ C2
derived, HallC3×C37 ⋊ C2×C5×C17
HallC5×C17×C37 ⋊ D3
HallC3×C17×C37 ⋊ C2×C5
HallC17×C37 ⋊ C5×D3
HallC3×C5×C37 ⋊ C2×C17
HallC3×C5×C17 ⋊ D37
HallC5×C37 ⋊ D3×C17
HallC3×C17 ⋊ C5×D37
SylowC37 ⋊ C5×D3×C17
HallC3×C5 ⋊ C17×D37
SylowC3 ⋊ C5×C17×D37

Subgroups

subgroupG/H
center, hypercenterC5×C17D111
commutator, cosocle, hypocenterC3×C37C2×C5×C17
FrattiniC1G
Fitting, socleC3×C5×C17×C37C2
LCSG ▷ C3×C37
UCSC1 ◁ C5×C17

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9435

Conjugacy classes & character table

4845 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×D3×C17×D37, C5×D17×D111, C5×D51⋊D37, …
maximal normal subgroup ofC5×D3×C17×D37, C5×D17×D111, C5×D51⋊D37, …
maximal quotient ofC5×C17×Dic111, C2×C5×C17×D111

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18870, 11);