Finite Group Databasebeta

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Dic3×C25×C53 #30629670

order15900
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C4×C25×C53 · Schur multiplier (H2) = C1

Aliases

direct productDic3×C25×C53
unambiguous semidirect productC3⋊(C4×C25×C53)

Splittings

derived, SylowC3 ⋊ C4×C25×C53
HallC3×C25×C53 ⋊ C4
HallC3×C53 ⋊ C4×C25
HallC3×C25 ⋊ C4×C53

Subgroups

subgroupG/H
center, hypercenterC2×C25×C53D3
commutator, hypocenterC3C4×C25×C53
FrattiniC2×C5C5×D3×C53
FittingC2×C3×C25×C53C2
socle, prime radicalC2×C3×C5×C53C2×C5
cosocleC2×C3×C5C2×C5×C53
LCSG ▷ C3
UCSC1 ◁ C2×C25×C53

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15900

Conjugacy classes & character table

7950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15900, 5);