Finite Group Databasebeta

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C3×Dic3×C23×C31 #38787304

order25668
automorphism?
homologyAbelianization (H1) = C3×C4×C23×C31 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic3×C23×C31
unambiguous semidirect productC3⋊(C3×C4×C23×C31)

Splittings

derivedC3 ⋊ C3×C4×C23×C31
HallC32×C23×C31 ⋊ C4
HallC32×C31 ⋊ C4×C23
HallC32×C23 ⋊ C4×C31
SylowC32 ⋊ C4×C23×C31

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23×C31D3
commutator, hypocenterC3C3×C4×C23×C31
FrattiniC2C3×D3×C23×C31
Fitting, socle, prime radicalC2×C32×C23×C31C2
cosocleC2×C3C2×C3×C23×C31
LCSG ▷ C3
UCSC1 ◁ C2×C3×C23×C31

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8556

Conjugacy classes & character table

12834 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25668, 51);