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C3×C7×Dic407 #46803136

order34188
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC3×C7×Dic407
unambiguous semidirect productC11⋊(C3×C7×Dic37)

Splittings

derived, HallC11×C37 ⋊ C3×C4×C7
HallC3×C7×C11×C37 ⋊ C4
HallC7×C11×C37 ⋊ C3×C4
HallC3×C11×C37 ⋊ C4×C7
HallC3×C7×C37 ⋊ Dic11
HallC7×C37 ⋊ C3×Dic11
HallC3×C7×C11 ⋊ Dic37
HallC3×C37 ⋊ C7×Dic11
HallC7×C11 ⋊ C3×Dic37
SylowC37 ⋊ C3×C7×Dic11
HallC3×C11 ⋊ C7×Dic37
SylowC11 ⋊ C3×C7×Dic37

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D407
commutator, hypocenterC11×C37C3×C4×C7
FrattiniC2C3×C7×D407
Fitting, socle, prime radicalC2×C3×C7×C11×C37C2
cosocleC2×C11×C37C2×C3×C7
LCSG ▷ C11×C37
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34188

Conjugacy classes & character table

8610 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 8);