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C4×C49×C37⋊C3 #36344161

order21756
automorphism?
homologyAbelianization (H1) = C3×C4×C49 · Schur multiplier (H2) = C1

Aliases

direct productC4×C49×C37⋊C3
unambiguous semidirect product(C4×C37)⋊(C3×C49)

Splittings

Fitting, HallC4×C37×C49 ⋊ C3
derived, SylowC37 ⋊ C3×C4×C49
HallC37×C49 ⋊ C3×C4
HallC4×C37 ⋊ C3×C49

Subgroups

subgroupG/H
center, hypercenterC4×C49C37⋊C3
commutator, hypocenterC37C3×C4×C49
FrattiniC2×C7C2×C7×C37⋊C3
FittingC4×C37×C49C3
socle, cosocleC2×C7×C37C2×C3×C7
prime radicalC2×C7×C37⋊C3C2×C7
LCSG ▷ C37
UCSC1 ◁ C4×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 7252

Conjugacy classes & character table

2940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21756, 14);