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C22×C25×C109⋊C3 #45658207

order32700
automorphism?
homologyAbelianization (H1) = C22×C3×C25 · Schur multiplier (H2) = C2

Aliases

direct productC22×C25×C109⋊C3

Splittings

Fitting, HallC22×C25×C109 ⋊ C3
derived, SylowC109 ⋊ C22×C3×C25
HallC25×C109 ⋊ C22×C3
HallC22×C109 ⋊ C3×C25

Subgroups

subgroupG/H
center, hypercenterC22×C25C109⋊C3
commutator, hypocenterC109C22×C3×C25
FrattiniC5C22×C5×C109⋊C3
FittingC22×C25×C109C3
socleC22×C5×C109C3×C5
prime radicalC22×C5×C109⋊C3C5
cosocleC5×C109C22×C3×C5
LCSG ▷ C109
UCSC1 ◁ C22×C25

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10900

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(32700, 43);