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Dic9×C31⋊C25 #42124258

order27900
automorphism?
homologyAbelianization (H1) = C4×C25 · Schur multiplier (H2) = C1

Aliases

direct productDic9×C31⋊C25
unambiguous semidirect productC9⋊(C4×C31⋊C25)
unambiguous semidirect product(C31×Dic9)⋊C25

Splittings

derived, HallC9×C31 ⋊ C4×C25
HallC9×C31⋊C25 ⋊ C4
HallC31×Dic9 ⋊ C25
SylowC31 ⋊ C25×Dic9
SylowC9 ⋊ C4×C31⋊C25

Subgroups

subgroupG/H
center, hypercenterC2×C5D9×ΓL(1,𝔽32)
commutator, hypocenterC9×C31C4×C25
FrattiniC2×C3×C5D3×ΓL(1,𝔽32)
Fitting, cosocleC2×C5×C9×C31C2×C5
socle, prime radicalC2×C3×C5×C31C5×D3
LCSG ▷ C9×C31
UCSC1 ◁ C2×C5

54 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

660 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 5);