Finite Group Databasebeta

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C3×Dic15×C101 #32911428

order18180
isoclinismisoclinic class of D15
automorphism?
homologyAbelianization (H1) = C3×C4×C101 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic15×C101
unambiguous semidirect productC3⋊(C3×Dic5×C101)

Splittings

derivedC3×C5 ⋊ C3×C4×C101
HallC32×C5×C101 ⋊ C4
HallC32×C101 ⋊ Dic5
HallC5×C101 ⋊ C3×Dic3
HallC32×C5 ⋊ C4×C101
SylowC32 ⋊ Dic5×C101
SylowC5 ⋊ C3×Dic3×C101

Subgroups

subgroupG/H
center, hypercenterC2×C3×C101D15
commutator, hypocenterC3×C5C3×C4×C101
FrattiniC2C3×D15×C101
Fitting, socle, prime radicalC2×C32×C5×C101C2
cosocleC2×C3×C5C2×C3×C101
LCSG ▷ C3×C5
UCSC1 ◁ C2×C3×C101

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6060

Conjugacy classes & character table

5454 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18180, 61);