Finite Group Databasebeta

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C3×C52×Dic3×C31 #42124663

order27900
isoclinismisoclinic class of D3
automorphism?
homologyAbelianization (H1) = C3×C4×C52×C31 · Schur multiplier (H2) = C5

Aliases

direct productC3×C52×Dic3×C31
unambiguous semidirect productC3⋊(C3×C4×C52×C31)

Splittings

derivedC3 ⋊ C3×C4×C52×C31
HallC32×C52×C31 ⋊ C4
HallC32×C31 ⋊ C4×C52
HallC32×C52 ⋊ C4×C31
SylowC32 ⋊ C4×C52×C31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C52×C31D3
commutator, hypocenterC3C3×C4×C52×C31
FrattiniC2C3×C52×D3×C31
Fitting, socle, prime radicalC2×C32×C52×C31C2
cosocleC2×C3C2×C3×C52×C31
LCSG ▷ C3
UCSC1 ◁ C2×C3×C52×C31

224 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

13950 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(27900, 410);