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C3×C22⋊((C31⋊C3)⋊C25) #42124393

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

Aliases

direct productC3×C22⋊((C31⋊C3)⋊C25)
unambiguous semidirect product(C22×C3)⋊((C31⋊C3)⋊C25)
unambiguous semidirect product(C3×C22⋊(C31⋊C3))⋊C25
unambiguous semidirect product(C3×C31⋊C25)⋊A4

Splittings

derived, HallC22×C31 ⋊ C32×C25
HallC22×C31⋊C25 ⋊ C32
HallC3×C22⋊(C31⋊C3) ⋊ C25
HallC31⋊C25 ⋊ C3×A4
SylowC31 ⋊ C3×A4×C25
SylowC22 ⋊ C3×(C31⋊C3)⋊C25

Subgroups

subgroupG/H
center, hypercenterC3×C5C22⋊((C31⋊C3)⋊C5)
commutator, hypocenterC22×C31C32×C25
FrattiniC5C3×C22⋊((C31⋊C3)⋊C5)
Fitting, socleC22×C3×C5×C31C3×C5
prime radicalC3×C5×C22⋊(C31⋊C3)C5
cosocleC22×C5×C31C32×C5
LCSG ▷ C22×C31
UCSC1 ◁ C3×C5

84 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

420 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 140);