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C4×C11×#66524 #28410787

order14652
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC4×C11×#66524

Splittings

derived, SylowC37 ⋊ C4×C9×C11
HallC4×C11×C37 ⋊ C9
HallC11×C37 ⋊ C4×C9
HallC4×C37 ⋊ C9×C11

Subgroups

subgroupG/H
center, hypercenterC3×C4×C11C37⋊C3
commutator, hypocenterC37C4×C9×C11
FrattiniC2×C3C2×C11×C37⋊C3
FittingC3×C4×C11×C37C3
socle, prime radicalC2×C3×C11×C37C2×C3
cosocleC2×C3×C37C2×C3×C11
LCSG ▷ C37
UCSC1 ◁ C3×C4×C11

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 14652

Conjugacy classes & character table

1980 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(14652, 2);