Finite Group Databasebeta

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C3×C19×Dic85 #34084296

order19380
automorphism?
homologyAbelianization (H1) = C3×C4×C19 · Schur multiplier (H2) = C1

Aliases

direct productC3×C19×Dic85

Splittings

derived, HallC5×C17 ⋊ C3×C4×C19
HallC3×C5×C17×C19 ⋊ C4
HallC5×C17×C19 ⋊ C3×C4
HallC3×C17×C19 ⋊ Dic5
HallC17×C19 ⋊ C3×Dic5
HallC3×C5×C19 ⋊ Dic17
HallC3×C5×C17 ⋊ C4×C19
HallC5×C19 ⋊ C3×Dic17
HallC3×C17 ⋊ C19×Dic5
SylowC17 ⋊ C3×C19×Dic5
HallC3×C5 ⋊ C19×Dic17
SylowC5 ⋊ C3×C19×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C3×C19D85
commutator, hypocenterC5×C17C3×C4×C19
FrattiniC2C3×C19×D85
Fitting, socle, prime radicalC2×C3×C5×C17×C19C2
cosocleC2×C5×C17C2×C3×C19
LCSG ▷ C5×C17
UCSC1 ◁ C2×C3×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19380

Conjugacy classes & character table

5016 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 8);