Finite Group Databasebeta

← Prev (#34062201) Next (#34062203) →

C3×C72×D5×C13 #34062202

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C72×C13 · Schur multiplier (H2) = C7

Aliases

direct productC3×C72×D5×C13
unambiguous semidirect productC5⋊(C2×C3×C72×C13)

Splittings

Fitting, socle, HallC3×C5×C72×C13 ⋊ C2
derived, SylowC5 ⋊ C2×C3×C72×C13
HallC5×C72×C13 ⋊ C2×C3
HallC3×C5×C72 ⋊ C2×C13
HallC5×C72 ⋊ C2×C3×C13
HallC3×C5×C13 ⋊ C2×C72
HallC5×C13 ⋊ C2×C3×C72
HallC3×C5 ⋊ C2×C72×C13

Subgroups

subgroupG/H
center, hypercenterC3×C72×C13D5
commutator, cosocle, hypocenterC5C2×C3×C72×C13
FrattiniC1G
Fitting, socleC3×C5×C72×C13C2
LCSG ▷ C5
UCSC1 ◁ C3×C72×C13

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9555

Conjugacy classes & character table

7644 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC3×C72×C13×AGL(1,𝔽5), C3×C72×#63120, C3×C7×C13×C7⋊AGL(1,𝔽5), …
maximal normal subgroup ofC3×C72×C13×AGL(1,𝔽5), C3×C72×#63120, C3×C7×C13×C7⋊AGL(1,𝔽5), …
maximal quotient ofC3×C72×C13×Dic5, C2×C3×C72×D5×C13

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 195);