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C2×C5×C49×D31 #44477127

order30380
automorphism?
homologyAbelianization (H1) = C22×C5×C49 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C49×D31

Splittings

FittingC2×C5×C31×C49 ⋊ C2
derived, SylowC31 ⋊ C22×C5×C49
HallC5×C31×C49 ⋊ C22
HallC31×C49 ⋊ C22×C5
HallC5×C31 ⋊ C22×C49

Subgroups

subgroupG/H
center, hypercenterC2×C5×C49D31
commutator, hypocenterC31C22×C5×C49
FrattiniC7C2×C5×C7×D31
FittingC2×C5×C31×C49C2
socleC2×C5×C7×C31C2×C7
prime radicalC2×C5×C7×D31C7
cosocleC7×C31C22×C5×C7
LCSG ▷ C31
UCSC1 ◁ C2×C5×C49

60 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 15190

Conjugacy classes & character table

8330 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30380, 36);