Finite Group Databasebeta

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C3×C4×C52×C31⋊C3 #42124651

order27900
isoclinismisoclinic class of C31⋊C3
automorphism?
homologyAbelianization (H1) = C32×C4×C52 · Schur multiplier (H2) = C3×C5

Aliases

direct productC3×C4×C52×C31⋊C3

Splittings

FittingC3×C4×C52×C31 ⋊ C3
derived, SylowC31 ⋊ C32×C4×C52
HallC4×C52×C31 ⋊ C32
HallC52×C31 ⋊ C32×C4
HallC4×C31 ⋊ C32×C52

Subgroups

subgroupG/H
center, hypercenterC3×C4×C52C31⋊C3
commutator, hypocenterC31C32×C4×C52
FrattiniC2C2×C3×C52×C31⋊C3
FittingC3×C4×C52×C31C3
socleC2×C3×C52×C31C2×C3
prime radicalC2×C3×C52×C31⋊C3C2
cosocleC2×C31C2×C32×C52
LCSG ▷ C31
UCSC1 ◁ C3×C4×C52

288 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3900 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 398);