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C5×C31×Dic51 #44539257

order31620
automorphism?
homologyAbelianization (H1) = C4×C5×C31 · Schur multiplier (H2) = C1

Aliases

direct productC5×C31×Dic51
unambiguous semidirect productC3⋊(C5×C31×Dic17)

Splittings

derived, HallC3×C17 ⋊ C4×C5×C31
HallC3×C5×C17×C31 ⋊ C4
HallC5×C17×C31 ⋊ Dic3
HallC3×C17×C31 ⋊ C4×C5
HallC17×C31 ⋊ C5×Dic3
HallC3×C5×C31 ⋊ Dic17
HallC3×C5×C17 ⋊ C4×C31
HallC3×C31 ⋊ C5×Dic17
HallC5×C17 ⋊ Dic3×C31
SylowC17 ⋊ C5×Dic3×C31
HallC3×C5 ⋊ C31×Dic17
SylowC3 ⋊ C5×C31×Dic17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C31D51
commutator, hypocenterC3×C17C4×C5×C31
FrattiniC2C5×C31×D51
Fitting, socle, prime radicalC2×C3×C5×C17×C31C2
cosocleC2×C3×C17C2×C5×C31
LCSG ▷ C3×C17
UCSC1 ◁ C2×C5×C31

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 31620

Conjugacy classes & character table

8370 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31620, 14);