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C3×Dic305⋊C5 #32912954

order18300
automorphism?
homologyAbelianization (H1) = C3×C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic305⋊C5
unambiguous semidirect product(C3×Dic305)⋊C5

Splittings

derivedC5×C61 ⋊ C3×C4×C5
HallC3×C5×C61⋊C5 ⋊ C4
HallC5×C61⋊C5 ⋊ C3×C4
HallC3×C61 ⋊ C5×Dic5
SylowC61 ⋊ C3×C5×Dic5

Subgroups

subgroupG/H
center, hypercenterC2×C3C5⋊(D61⋊C5)
commutator, hypocenterC5×C61C3×C4×C5
FrattiniC2C3×C5⋊(D61⋊C5)
Fitting, socleC2×C3×C5×C61C2×C5
prime radicalC2×C3×C5×C61⋊C5C2
cosocleC2×C5×C61C2×C3×C5
LCSG ▷ C5×C61
UCSC1 ◁ C2×C3

64 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3660

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 77);