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C11×C37×Dic21 #46803145

order34188
automorphism?
homologyAbelianization (H1) = C4×C11×C37 · Schur multiplier (H2) = C1

Aliases

direct productC11×C37×Dic21
unambiguous semidirect productC3⋊(C11×Dic7×C37)
unambiguous semidirect productC7⋊(C11×Dic3×C37)

Splittings

derived, HallC3×C7 ⋊ C4×C11×C37
HallC3×C7×C11×C37 ⋊ C4
HallC7×C11×C37 ⋊ Dic3
HallC3×C11×C37 ⋊ Dic7
HallC3×C7×C37 ⋊ C4×C11
HallC7×C37 ⋊ C11×Dic3
HallC3×C7×C11 ⋊ C4×C37
HallC3×C37 ⋊ C11×Dic7
HallC7×C11 ⋊ Dic3×C37
HallC3×C11 ⋊ Dic7×C37
SylowC7 ⋊ C11×Dic3×C37
SylowC3 ⋊ C11×Dic7×C37

Subgroups

subgroupG/H
center, hypercenterC2×C11×C37D21
commutator, hypocenterC3×C7C4×C11×C37
FrattiniC2C11×C37×D21
Fitting, socle, prime radicalC2×C3×C7×C11×C37C2
cosocleC2×C3×C7C2×C11×C37
LCSG ▷ C3×C7
UCSC1 ◁ C2×C11×C37

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 34188

Conjugacy classes & character table

9768 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(34188, 17);