Finite Group Databasebeta

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C3×C5×C13×D19 #20301799

order7410
isoclinismisoclinic class of D19
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C13 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×C13×D19

Splittings

Fitting, socle, HallC3×C5×C13×C19 ⋊ C2
derived, SylowC19 ⋊ C2×C3×C5×C13
HallC5×C13×C19 ⋊ C2×C3
HallC3×C13×C19 ⋊ C2×C5
HallC3×C5×C19 ⋊ C2×C13
HallC13×C19 ⋊ C2×C3×C5
HallC5×C19 ⋊ C2×C3×C13
HallC3×C19 ⋊ C2×C5×C13

Subgroups

subgroupG/H
center, hypercenterC3×C5×C13D19
commutator, hypocenterC19C2×C3×C5×C13
FrattiniC1G
Fitting, socleC3×C5×C13×C19C2
LCSG ▷ C19
UCSC1 ◁ C3×C5×C13

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2145 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C5×D13×D19, C3×D5×C13×D19, C3×D19×D65, …
maximal normal subgroup ofC3×C5×D13×D19, C3×D5×C13×D19, C3×D19×D65, …
maximal quotient ofC3×C5×C13×Dic19, C2×C3×C5×C13×D19, C5×C9×C13×D19, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7410, 6);