Finite Group Databasebeta

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C32×C5×Dic31⋊C5 #42124607

order27900
automorphism?
homologyAbelianization (H1) = C32×C4×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC32×C5×Dic31⋊C5
unambiguous semidirect product(C32×Dic31)⋊C52
unambiguous semidirect product(C32×C5×Dic31)⋊C5

Splittings

derived, SylowC31 ⋊ C32×C4×C52
HallC32×C5×ΓL(1,𝔽32) ⋊ C4
HallC32×Dic31 ⋊ C52
HallC5×ΓL(1,𝔽32) ⋊ C32×C4
HallC32×C31 ⋊ C4×C52
HallDic31 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC2×C32×C5D31⋊C5
commutator, hypocenterC31C32×C4×C52
FrattiniC2C32×C5×D31⋊C5
Fitting, socleC2×C32×C5×C31C2×C5
prime radicalC2×C32×C5×ΓL(1,𝔽32)C2
cosocleC2×C31C2×C32×C52
LCSG ▷ C31
UCSC1 ◁ C2×C32×C5

288 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1170 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 354);