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C5×C37×Dic49 #49136357

order36260
automorphism?
homologyAbelianization (H1) = C4×C5×C37 · Schur multiplier (H2) = C1

Aliases

direct productC5×C37×Dic49
unambiguous semidirect productC49⋊(C4×C5×C37)

Splittings

derived, SylowC49 ⋊ C4×C5×C37
HallC5×C37×C49 ⋊ C4
HallC37×C49 ⋊ C4×C5
HallC5×C49 ⋊ C4×C37

Subgroups

subgroupG/H
center, hypercenterC2×C5×C37D49
commutator, hypocenterC49C4×C5×C37
FrattiniC2×C7C5×D7×C37
FittingC2×C5×C37×C49C2
socle, prime radicalC2×C5×C7×C37D7
cosocleC2×C49C2×C5×C37
LCSG ▷ C49
UCSC1 ◁ C2×C5×C37

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36260

Conjugacy classes & character table

9620 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36260, 3);