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C5×#16809810 #30680800

order16770
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#16809810

Splittings

Fitting, socle, HallC5×C13×C43 ⋊ C2×C3
derived, HallC13×C43 ⋊ C2×C3×C5
HallC5×#13131975 ⋊ C2
HallC5×C13×D43 ⋊ C3
Hall#13131975 ⋊ C2×C5
HallC13×D43 ⋊ C3×C5
HallC5×D43 ⋊ C13⋊C3
HallC5×C43 ⋊ C2×C13⋊C3
HallD43 ⋊ C5×C13⋊C3
HallC5×C13 ⋊ D43⋊C3
SylowC43 ⋊ C2×C5×C13⋊C3
SylowC13 ⋊ C5×D43⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#16809810
commutator, cosocle, hypocenterC13×C43C2×C3×C5
FrattiniC1G
Fitting, socleC5×C13×C43C2×C3
LCSG ▷ C13×C43
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2795

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#16809810⋊C2, #16809810⋊D5, D5×#16809810, …
maximal normal subgroup ofC5×#16809810⋊C2, #16809810⋊D5, D5×#16809810, …
maximal quotient ofC5×#20269436, C2×C5×#16809810

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16770, 24);