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C3×C23⋊((C31⋊C3)⋊C4) #38787290

order25668
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C23⋊((C31⋊C3)⋊C4)
unambiguous semidirect productC23⋊(C3×(C31⋊C3)⋊C4)
unambiguous semidirect product(C31⋊C3)⋊(C3×Dic23)
unambiguous semidirect productDic713⋊C32
unambiguous semidirect product(C3×Dic713)⋊C3

Splittings

derived, HallC23×C31 ⋊ C32×C4
HallC3×C23×C31⋊C3 ⋊ C4
HallDic713 ⋊ C32
HallC3×C31⋊C3 ⋊ Dic23
SylowC31 ⋊ C32×Dic23
SylowC23 ⋊ C3×(C31⋊C3)⋊C4

Subgroups

subgroupG/H
center, hypercenterC2×C3C23⋊(D31⋊C3)
commutator, hypocenterC23×C31C32×C4
FrattiniC2C3×C23⋊(D31⋊C3)
Fitting, socleC2×C3×C23×C31C2×C3
prime radicalC2×C3×C23×C31⋊C3C2
cosocleC2×C23×C31C2×C32
LCSG ▷ C23×C31
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8556

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25668, 37);