Finite Group Databasebeta

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C3×C5×Dic3×C173 #44528155

order31140
automorphism?
homologyAbelianization (H1) = C3×C4×C5×C173 · Schur multiplier (H2) = C1

Aliases

direct productC3×C5×Dic3×C173
unambiguous semidirect productC3⋊(C3×C4×C5×C173)

Splittings

derivedC3 ⋊ C3×C4×C5×C173
HallC32×C5×C173 ⋊ C4
HallC32×C173 ⋊ C4×C5
HallC32×C5 ⋊ C4×C173
SylowC32 ⋊ C4×C5×C173

Subgroups

subgroupG/H
center, hypercenterC2×C3×C5×C173D3
commutator, hypocenterC3C3×C4×C5×C173
FrattiniC2C3×C5×D3×C173
Fitting, socle, prime radicalC2×C32×C5×C173C2
cosocleC2×C3C2×C3×C5×C173
LCSG ▷ C3
UCSC1 ◁ C2×C3×C5×C173

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10380

Conjugacy classes & character table

15570 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31140, 45);