Finite Group Databasebeta

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C5×#20293712 #46806209

order34410
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×#20293712

Splittings

Fitting, socle, HallC5×C31×C37 ⋊ C2×C3
derived, HallC31×C37 ⋊ C2×C3×C5
HallC5×#16812215 ⋊ C2
HallC5×C37×D31 ⋊ C3
Hall#16812215 ⋊ C2×C5
HallC37×D31 ⋊ C3×C5
HallC5×D31 ⋊ C37⋊C3
HallC5×C37 ⋊ D31⋊C3
HallC5×C31 ⋊ C2×C37⋊C3
HallD31 ⋊ C5×C37⋊C3
SylowC37 ⋊ C5×D31⋊C3
SylowC31 ⋊ C2×C5×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC5#20293712
commutator, cosocle, hypocenterC31×C37C2×C3×C5
FrattiniC1G
Fitting, socleC5×C31×C37C2×C3
LCSG ▷ C31×C37
UCSC1 ◁ C5

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5735

Conjugacy classes & character table

1075 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34410, 39);