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C2×C3⋊(D61⋊C25) #32912913

order18300
automorphism?
homologyAbelianization (H1) = C22×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C3⋊(D61⋊C25)
unambiguous semidirect product(C2×C3)⋊(D61⋊C25)
unambiguous semidirect product(C2×D183)⋊C25
unambiguous semidirect product(C2×C61⋊C25)⋊D3

Splittings

derived, HallC3×C61 ⋊ C22×C25
HallC3×C61⋊C25 ⋊ C22
HallC61⋊C25 ⋊ C2×D3
HallC2×D183 ⋊ C25
SylowC61 ⋊ C2×D3×C25
SylowC3 ⋊ C2×D61⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5C3⋊(D61⋊C5)
commutator, hypocenterC3×C61C22×C25
FrattiniC5C2×C3⋊(D61⋊C5)
Fitting, socleC2×C3×C5×C61C2×C5
prime radicalC2×C5×D183C5
cosocleC3×C5×C61C22×C5
LCSG ▷ C3×C61
UCSC1 ◁ C2×C5

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 9150

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(18300, 36);