Finite Group Databasebeta

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C5×Dic1887 #49179758

order37740
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic1887
unambiguous semidirect productC3⋊(C5×Dic629)

Splittings

derived, HallC3×C17×C37 ⋊ C4×C5
HallC3×C5×C17×C37 ⋊ C4
HallC5×C17×C37 ⋊ Dic3
HallC17×C37 ⋊ C5×Dic3
HallC3×C5×C37 ⋊ Dic17
HallC3×C5×C17 ⋊ Dic37
HallC5×C37 ⋊ Dic51
HallC3×C37 ⋊ C5×Dic17
HallC5×C17 ⋊ Dic111
HallC3×C17 ⋊ C5×Dic37
SylowC37 ⋊ C5×Dic51
SylowC17 ⋊ C5×Dic111
HallC3×C5 ⋊ Dic629
SylowC3 ⋊ C5×Dic629

Subgroups

subgroupG/H
center, hypercenterC2×C5D1887
commutator, hypocenterC3×C17×C37C4×C5
FrattiniC2C5×D1887
Fitting, socle, prime radicalC2×C3×C5×C17×C37C2
cosocleC2×C3×C17×C37C2×C5
LCSG ▷ C3×C17×C37
UCSC1 ◁ C2×C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37740

Conjugacy classes & character table

9450 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37740, 13);