Finite Group Databasebeta

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C3×C17×Dic185 #49179752

order37740
automorphism?
homologyAbelianization (H1) = C3×C4×C17 · Schur multiplier (H2) = C1

Aliases

direct productC3×C17×Dic185

Splittings

derived, HallC5×C37 ⋊ C3×C4×C17
HallC3×C5×C17×C37 ⋊ C4
HallC5×C17×C37 ⋊ C3×C4
HallC3×C17×C37 ⋊ Dic5
HallC17×C37 ⋊ C3×Dic5
HallC3×C5×C37 ⋊ C4×C17
HallC3×C5×C17 ⋊ Dic37
HallC3×C37 ⋊ C17×Dic5
HallC5×C17 ⋊ C3×Dic37
SylowC37 ⋊ C3×C17×Dic5
HallC3×C5 ⋊ C17×Dic37
SylowC5 ⋊ C3×C17×Dic37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C17D185
commutator, hypocenterC5×C37C3×C4×C17
FrattiniC2C3×C17×D185
Fitting, socle, prime radicalC2×C3×C5×C17×C37C2
cosocleC2×C5×C37C2×C3×C17
LCSG ▷ C5×C37
UCSC1 ◁ C2×C3×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 37740

Conjugacy classes & character table

9588 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(37740, 7);