Finite Group Databasebeta

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C22×C3×C25×C37⋊C3 #45685925

order33300
automorphism?
homologyAbelianization (H1) = C22×C32×C25 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×C25×C37⋊C3

Splittings

FittingC22×C3×C25×C37 ⋊ C3
derived, SylowC37 ⋊ C22×C32×C25
HallC22×C25×C37 ⋊ C32
HallC25×C37 ⋊ C22×C32
HallC22×C37 ⋊ C32×C25

Subgroups

subgroupG/H
center, hypercenterC22×C3×C25C37⋊C3
commutator, hypocenterC37C22×C32×C25
FrattiniC5C22×C3×C5×C37⋊C3
FittingC22×C3×C25×C37C3
socleC22×C3×C5×C37C3×C5
prime radicalC22×C3×C5×C37⋊C3C5
cosocleC5×C37C22×C32×C5
LCSG ▷ C37
UCSC1 ◁ C22×C3×C25

180 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11100

Conjugacy classes & character table

4500 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(33300, 198);