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C2×(C5⋊D5)⋊#66524 #45685992

order33300
automorphism?
homologyAbelianization (H1) = C22×C9 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×(C5⋊D5)⋊#66524
unambiguous semidirect product(C2×C5⋊D5)⋊#66524

Splittings

derived, HallC52×C37 ⋊ C22×C9
HallC52⋊#66524 ⋊ C22
HallC2×C37×C5⋊D5 ⋊ C9
HallC2×C5⋊D5 ⋊ #66524
SylowC37 ⋊ C2×(C5⋊D5)⋊C9
SylowC52 ⋊ C22×#66524

Subgroups

subgroupG/H
center, hypercenterC2×C3(C5⋊D5)⋊(C37⋊C3)
commutator, hypocenterC52×C37C22×C9
FrattiniC3C2×(C5⋊D5)⋊(C37⋊C3)
Fitting, socleC2×C3×C52×C37C2×C3
prime radicalC2×C3×C37×C5⋊D5C3
cosocleC3×C52×C37C22×C3
LCSG ▷ C52×C37
UCSC1 ◁ C2×C3

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3330

Conjugacy classes & character table

1068 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 265);