Finite Group Databasebeta

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C19×Dic255 #34084304

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

Aliases

direct productC19×Dic255
unambiguous semidirect productC3⋊(C19×Dic85)

Splittings

derived, HallC3×C5×C17 ⋊ C4×C19
HallC3×C5×C17×C19 ⋊ C4
HallC5×C17×C19 ⋊ Dic3
HallC3×C17×C19 ⋊ Dic5
HallC17×C19 ⋊ Dic15
HallC3×C5×C19 ⋊ Dic17
HallC5×C19 ⋊ Dic51
HallC5×C17 ⋊ Dic3×C19
HallC3×C19 ⋊ Dic85
HallC3×C17 ⋊ C19×Dic5
SylowC17 ⋊ C19×Dic15
HallC3×C5 ⋊ C19×Dic17
SylowC5 ⋊ C19×Dic51
SylowC3 ⋊ C19×Dic85

Subgroups

subgroupG/H
center, hypercenterC2×C19D255
commutator, hypocenterC3×C5×C17C4×C19
FrattiniC2C19×D255
Fitting, socle, prime radicalC2×C3×C5×C17×C19C2
cosocleC2×C3×C5×C17C2×C19
LCSG ▷ C3×C5×C17
UCSC1 ◁ C2×C19

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 19380

Conjugacy classes & character table

4902 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(19380, 16);