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C23×C3⋊((C31⋊C3)⋊C4) #38787292

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

Aliases

direct productC23×C3⋊((C31⋊C3)⋊C4)
unambiguous semidirect productC3⋊(C23×(C31⋊C3)⋊C4)
unambiguous semidirect product(C31⋊C3)⋊(Dic3×C23)
unambiguous semidirect productDic93⋊(C3×C23)
unambiguous semidirect product(C23×Dic93)⋊C3

Splittings

derivedC3×C31 ⋊ C3×C4×C23
HallC3×C23×C31⋊C3 ⋊ C4
HallC23×C31 ⋊ C3×Dic3
HallC3×C31⋊C3 ⋊ C4×C23
SylowC31 ⋊ C3×Dic3×C23

Subgroups

subgroupG/H
center, hypercenterC2×C23C3⋊(D31⋊C3)
commutator, hypocenterC3×C31C3×C4×C23
FrattiniC2C23×C3⋊(D31⋊C3)
Fitting, socleC2×C3×C23×C31C2×C3
prime radicalC2×C3×C23×C31⋊C3C2
cosocleC2×C3×C31C2×C3×C23
LCSG ▷ C3×C31
UCSC1 ◁ C2×C23

56 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8556

Conjugacy classes & character table

1104 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25668, 39);