Finite Group Databasebeta

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C3×C23⋊(Dic37⋊C3) #44499644

order30636
automorphism?
homologyAbelianization (H1) = C32×C4 · Schur multiplier (H2) = C3

Aliases

direct productC3×C23⋊(Dic37⋊C3)
unambiguous semidirect productC23⋊(C3×Dic37⋊C3)
unambiguous semidirect productDic851⋊C32
unambiguous semidirect product(C3×Dic851)⋊C3

Splittings

derived, HallC23×C37 ⋊ C32×C4
HallC3×C23×C37⋊C3 ⋊ C4
HallDic851 ⋊ C32
HallC3×C37⋊C3 ⋊ Dic23
SylowC37 ⋊ C32×Dic23
SylowC23 ⋊ C3×Dic37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C3C23⋊(D37⋊C3)
commutator, hypocenterC23×C37C32×C4
FrattiniC2C3×C23⋊(D37⋊C3)
Fitting, socleC2×C3×C23×C37C2×C3
prime radicalC2×C3×C23×C37⋊C3C2
cosocleC2×C23×C37C2×C32
LCSG ▷ C23×C37
UCSC1 ◁ C2×C3

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 10212

Conjugacy classes & character table

1062 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30636, 47);