Finite Group Databasebeta

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C25×C31×C3⋊Dic3 #42124335

order27900
isoclinismisoclinic class of C3⋊D3
automorphism?
homologyAbelianization (H1) = C4×C25×C31 · Schur multiplier (H2) = C3

Aliases

direct productC25×C31×C3⋊Dic3
unambiguous semidirect productC3⋊(Dic3×C25×C31)

Splittings

derived, SylowC32 ⋊ C4×C25×C31
HallC32×C25×C31 ⋊ C4
HallC32×C31 ⋊ C4×C25
HallC32×C25 ⋊ C4×C31

Subgroups

subgroupG/H
center, hypercenterC2×C25×C31C3⋊D3
commutator, hypocenterC32C4×C25×C31
FrattiniC2×C5C5×C3⋊D3×C31
FittingC2×C32×C25×C31C2
socle, prime radicalC2×C32×C5×C31C2×C5
cosocleC2×C32×C5C2×C5×C31
LCSG ▷ C32
UCSC1 ◁ C2×C25×C31

108 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

9300 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 82);