Finite Group Databasebeta

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C5×#16838450 #34062074

order19110
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#16838450

Splittings

Fitting, socle, HallC5×C72×C13 ⋊ C2×C3
derived, HallC72×C13 ⋊ C2×C3×C5
HallC5×C13×#3861 ⋊ C2
HallC5×C7⋊D91 ⋊ C3
HallC13×#3861 ⋊ C2×C5
HallC7⋊D91 ⋊ C3×C5
HallC5×#3861 ⋊ D13
HallC5×C72 ⋊ C3×D13
Hall#3861 ⋊ C5×D13
HallC5×C13 ⋊ #64424
SylowC72 ⋊ C3×C5×D13
SylowC13 ⋊ C5×#64424

Subgroups

subgroupG/H
center, hypercenterC5#16838450
commutator, cosocle, hypocenterC72×C13C2×C3×C5
FrattiniC1G
Fitting, socleC5×C72×C13C2×C3
LCSG ▷ C72×C13
UCSC1 ◁ C5

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3185

Conjugacy classes & character table

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

Relationships

maximal subgroup ofC5×#21439682, C5×D13×#64424, C5×#64423⋊D13, …
maximal normal subgroup ofC5×#21439682, C5×D13×#64424, C5×#64423⋊D13, …
maximal quotient ofC5×#21439526, C2×C5×#16838450

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19110, 67);