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C7×C11×Dic111 #46803142

order34188
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×Dic111
unambiguous semidirect productC3⋊(C7×C11×Dic37)

Splittings

derived, HallC3×C37 ⋊ C4×C7×C11
HallC3×C7×C11×C37 ⋊ C4
HallC7×C11×C37 ⋊ Dic3
HallC3×C11×C37 ⋊ C4×C7
HallC3×C7×C37 ⋊ C4×C11
HallC11×C37 ⋊ C7×Dic3
HallC7×C37 ⋊ C11×Dic3
HallC3×C7×C11 ⋊ Dic37
SylowC37 ⋊ C7×C11×Dic3
HallC3×C11 ⋊ C7×Dic37
HallC3×C7 ⋊ C11×Dic37
SylowC3 ⋊ C7×C11×Dic37

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11D111
commutator, hypocenterC3×C37C4×C7×C11
FrattiniC2C7×C11×D111
Fitting, socle, prime radicalC2×C3×C7×C11×C37C2
cosocleC2×C3×C37C2×C7×C11
LCSG ▷ C3×C37
UCSC1 ◁ C2×C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34188

Conjugacy classes & character table

8778 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 14);