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C2×C37×(C5⋊D5)⋊C9 #45685990

order33300
automorphism?
homologyAbelianization (H1) = C22×C9×C37 · Schur multiplier (H2) = C2×C5

Aliases

direct productC2×C37×(C5⋊D5)⋊C9
unambiguous semidirect product(C2×C5⋊D5)⋊(C9×C37)

Splittings

derived, SylowC52 ⋊ C22×C9×C37
HallC37×C52⋊C9 ⋊ C22
HallC2×C37×C5⋊D5 ⋊ C9
HallC52×C37 ⋊ C22×C9
HallC52⋊C9 ⋊ C22×C37
HallC2×C5⋊D5 ⋊ C9×C37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C37(C5⋊D5)⋊C3
commutator, hypocenterC52C22×C9×C37
FrattiniC3C2×C37×(C5⋊D5)⋊C3
Fitting, socleC2×C3×C52×C37C2×C3
prime radicalC2×C3×C37×C5⋊D5C3
cosocleC3×C52C22×C3×C37
LCSG ▷ C52
UCSC1 ◁ C2×C3×C37

100 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3330

Conjugacy classes & character table

2220 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 263);