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C3×Dic2849 #46803140

order34188
automorphism?
homologyAbelianization (H1) = C3×C4 · Schur multiplier (H2) = C1

Aliases

direct productC3×Dic2849
unambiguous semidirect productC11⋊(C3×Dic259)

Splittings

derived, HallC7×C11×C37 ⋊ C3×C4
HallC3×C7×C11×C37 ⋊ C4
HallC3×C11×C37 ⋊ Dic7
HallC3×C7×C37 ⋊ Dic11
HallC11×C37 ⋊ C3×Dic7
HallC7×C37 ⋊ C3×Dic11
HallC3×C7×C11 ⋊ Dic37
HallC3×C37 ⋊ Dic77
HallC7×C11 ⋊ C3×Dic37
SylowC37 ⋊ C3×Dic77
HallC3×C11 ⋊ Dic259
HallC3×C7 ⋊ Dic407
SylowC11 ⋊ C3×Dic259
SylowC7 ⋊ C3×Dic407

Subgroups

subgroupG/H
center, hypercenterC2×C3D2849
commutator, hypocenterC7×C11×C37C3×C4
FrattiniC2C3×D2849
Fitting, socle, prime radicalC2×C3×C7×C11×C37C2
cosocleC2×C7×C11×C37C2×C3
LCSG ▷ C7×C11×C37
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34188

Conjugacy classes & character table

8556 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 12);