Finite Group Databasebeta

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C3×C19×Dic35 #22547586

order7980
isoclinismisoclinic class of D35
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19×Dic35

Splittings

derived, HallC5×C7 ⋊ C3×C4×C19
HallC3×C5×C7×C19 ⋊ C4
HallC5×C7×C19 ⋊ C3×C4
HallC3×C7×C19 ⋊ Dic5
HallC3×C5×C19 ⋊ Dic7
HallC7×C19 ⋊ C3×Dic5
HallC3×C5×C7 ⋊ C4×C19
HallC5×C19 ⋊ C3×Dic7
HallC3×C7 ⋊ C19×Dic5
HallC3×C5 ⋊ C19×Dic7
SylowC7 ⋊ C3×C19×Dic5
SylowC5 ⋊ C3×C19×Dic7

Subgroups

subgroupG/H
center, hypercenterC2×C3×C19D35
commutator, hypocenterC5×C7C3×C4×C19
FrattiniC2C3×C19×D35
Fitting, socleC2×C3×C5×C7×C19C2
LCSG ▷ C5×C7
UCSC1 ◁ C2×C3×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2166 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×C19×Dic35, Dic35×#4294, C19×(C7⋊C9)⋊Dic5, …
maximal normal subgroup ofC9×C19×Dic35, Dic35×#4294, C19×(C7⋊C9)⋊Dic5, …
maximal quotient ofC9×C19×Dic35, C3×C19×Dic105, C32×C19×Dic35

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7980, 11);