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C13×D645 #30680794

order16770
automorphism?
homologyAbelianization (H1) = C2×C13 · Schur multiplier (H2) = C1

Aliases

direct productC13×D645
unambiguous semidirect productC3⋊(C13×D215)
unambiguous semidirect productC5⋊(C13×D129)
unambiguous semidirect productC43⋊(C13×D15)

Splittings

Fitting, socle, HallC3×C5×C13×C43 ⋊ C2
derived, HallC3×C5×C43 ⋊ C2×C13
HallC5×C13×C43 ⋊ D3
HallC3×C13×C43 ⋊ D5
HallC13×C43 ⋊ D15
HallC5×C43 ⋊ D3×C13
HallC3×C5×C13 ⋊ D43
HallC3×C43 ⋊ D5×C13
HallC5×C13 ⋊ D129
SylowC43 ⋊ C13×D15
HallC3×C13 ⋊ D215
HallC3×C5 ⋊ C13×D43
SylowC5 ⋊ C13×D129
SylowC3 ⋊ C13×D215

Subgroups

subgroupG/H
center, hypercenterC13D645
commutator, cosocle, hypocenterC3×C5×C43C2×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C43C2
LCSG ▷ C3×C5×C43
UCSC1 ◁ C13

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8385

Conjugacy classes & character table

4212 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC13×D15×D43, D13×D645, D559⋊D15, …
maximal normal subgroup ofC13×D15×D43, D13×D645, D559⋊D15, …
maximal quotient ofC13×Dic645, C2×C13×D645

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16770, 18);