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C22×C3×(C31⋊C3)⋊C25 #42124392

order27900
automorphism?
homologyAbelianization (H1) = C22×C32×C25 · Schur multiplier (H2) = C2×C3

Aliases

direct productC22×C3×(C31⋊C3)⋊C25
unambiguous semidirect product(C22×C3×C31⋊C3)⋊C25

Splittings

derived, SylowC31 ⋊ C22×C32×C25
HallC22×C31⋊C25 ⋊ C32
HallC22×C3×C31⋊C3 ⋊ C25
HallC31⋊C25 ⋊ C22×C32
HallC3×C31⋊C3 ⋊ C22×C25
HallC22×C31 ⋊ C32×C25

Subgroups

subgroupG/H
center, hypercenterC22×C3×C5(C31⋊C3)⋊C5
commutator, hypocenterC31C22×C32×C25
FrattiniC5C22×C3×(C31⋊C3)⋊C5
Fitting, socleC22×C3×C5×C31C3×C5
prime radicalC22×C3×C5×C31⋊C3C5
cosocleC5×C31C22×C32×C5
LCSG ▷ C31
UCSC1 ◁ C22×C3×C5

180 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1020 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 139);