Finite Group Databasebeta

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C2×C9×C25×D37 #45685773

order33300
automorphism?
homologyAbelianization (H1) = C22×C9×C25 · Schur multiplier (H2) = C2

Aliases

direct productC2×C9×C25×D37

Splittings

FittingC2×C9×C25×C37 ⋊ C2
derived, SylowC37 ⋊ C22×C9×C25
HallC9×C25×C37 ⋊ C22
HallC25×C37 ⋊ C22×C9
HallC9×C37 ⋊ C22×C25

Subgroups

subgroupG/H
center, hypercenterC2×C9×C25D37
commutator, hypocenterC37C22×C9×C25
FrattiniC3×C5C2×C3×C5×D37
FittingC2×C9×C25×C37C2
socleC2×C3×C5×C37C2×C3×C5
prime radicalC2×C3×C5×D37C3×C5
cosocleC3×C5×C37C22×C3×C5
LCSG ▷ C37
UCSC1 ◁ C2×C9×C25

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16650

Conjugacy classes & character table

9000 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 46);