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C5×C49×Dic37 #49136356

order36260
automorphism?
homologyAbelianization (H1) = C4×C5×C49 · Schur multiplier (H2) = C1

Aliases

direct productC5×C49×Dic37

Splittings

derived, SylowC37 ⋊ C4×C5×C49
HallC5×C37×C49 ⋊ C4
HallC37×C49 ⋊ C4×C5
HallC5×C37 ⋊ C4×C49

Subgroups

subgroupG/H
center, hypercenterC2×C5×C49D37
commutator, hypocenterC37C4×C5×C49
FrattiniC2×C7C5×C7×D37
FittingC2×C5×C37×C49C2
socle, prime radicalC2×C5×C7×C37C2×C7
cosocleC2×C7×C37C2×C5×C7
LCSG ▷ C37
UCSC1 ◁ C2×C5×C49

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36260

Conjugacy classes & character table

9800 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36260, 2);