Finite Group Databasebeta

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C3×C23×(C31⋊C3)⋊C4 #38787289

order25668
automorphism?
homologyAbelianization (H1) = C32×C4×C23 · Schur multiplier (H2) = C3

Aliases

direct productC3×C23×(C31⋊C3)⋊C4
unambiguous semidirect product(C31⋊C3)⋊(C3×C4×C23)
unambiguous semidirect productDic31⋊(C32×C23)
unambiguous semidirect product(C3×Dic31)⋊(C3×C23)
unambiguous semidirect product(C23×Dic31)⋊C32
unambiguous semidirect product(C3×C23×Dic31)⋊C3

Splittings

derived, SylowC31 ⋊ C32×C4×C23
HallC3×C23×C31⋊C3 ⋊ C4
HallC23×Dic31 ⋊ C32
HallC23×C31 ⋊ C32×C4
HallC3×C31⋊C3 ⋊ C4×C23
HallDic31 ⋊ C32×C23

Subgroups

subgroupG/H
center, hypercenterC2×C3×C23D31⋊C3
commutator, hypocenterC31C32×C4×C23
FrattiniC2C3×C23×D31⋊C3
Fitting, socleC2×C3×C23×C31C2×C3
prime radicalC2×C3×C23×C31⋊C3C2
cosocleC2×C31C2×C32×C23
LCSG ▷ C31
UCSC1 ◁ C2×C3×C23

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 8556

Conjugacy classes & character table

1518 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25668, 36);