Finite Group Databasebeta

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C3×#27160385 #49179840

order37740
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×#27160385

Splittings

Fitting, socle, HallC3×C5×C17×C37 ⋊ C4
derived, HallC5×C17×C37 ⋊ C3×C4
HallC3×C17×C37 ⋊ Dic5
HallC17×C37 ⋊ C3×Dic5
HallC3×C5×C37 ⋊ #595
HallC3×C5×C17 ⋊ #3866
HallC5×C37 ⋊ C3×#595
HallC3×C37 ⋊ #66772
HallC5×C17 ⋊ C3×#3866
HallC3×C17 ⋊ #10625194
SylowC37 ⋊ C3×#66772
SylowC17 ⋊ C3×#10625194
HallC3×C5 ⋊ #14578980
SylowC5 ⋊ C3×#14578980

Subgroups

subgroupG/H
center, hypercenterC3#27160385
commutator, hypocenterC5×C17×C37C3×C4
FrattiniC1G
Fitting, socleC3×C5×C17×C37C4
prime radicalC3×C5×D629C2
cosocleC5×D629C2×C3
LCSG ▷ C5×C17×C37
UCSC1 ◁ C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9435

Conjugacy classes & character table

2379 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37740, 95);