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C2×C49×D117 #37524129

order22932
automorphism?
homologyAbelianization (H1) = C22×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C49×D117
unambiguous semidirect product(C2×C9)⋊(D13×C49)
unambiguous semidirect product(C2×C13)⋊(D9×C49)

Splittings

FittingC2×C9×C13×C49 ⋊ C2
derived, HallC9×C13 ⋊ C22×C49
HallC9×C13×C49 ⋊ C22
HallC13×C49 ⋊ C2×D9
HallC9×C49 ⋊ C2×D13
SylowC13 ⋊ C2×D9×C49
SylowC9 ⋊ C2×D13×C49

Subgroups

subgroupG/H
center, hypercenterC2×C49D117
commutator, hypocenterC9×C13C22×C49
FrattiniC3×C7C2×C7×D39
FittingC2×C9×C13×C49C2
socleC2×C3×C7×C13D3×C7
prime radicalC2×C7×D117C7
cosocleC7×C9×C13C22×C7
LCSG ▷ C9×C13
UCSC1 ◁ C2×C49

90 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 11466

Conjugacy classes & character table

5880 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(22932, 74);