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C5×Dic7×C121 #30683752

order16940
isoclinismisoclinic class of D7
automorphism?
homologyAbelianization (H1) = C4×C5×C121 · Schur multiplier (H2) = C1

Aliases

direct productC5×Dic7×C121
unambiguous semidirect productC7⋊(C4×C5×C121)

Splittings

derived, SylowC7 ⋊ C4×C5×C121
HallC5×C7×C121 ⋊ C4
HallC7×C121 ⋊ C4×C5
HallC5×C7 ⋊ C4×C121

Subgroups

subgroupG/H
center, hypercenterC2×C5×C121D7
commutator, hypocenterC7C4×C5×C121
FrattiniC2×C11C5×C11×D7
FittingC2×C5×C7×C121C2
socle, prime radicalC2×C5×C7×C11C2×C11
cosocleC2×C7×C11C2×C5×C11
LCSG ▷ C7
UCSC1 ◁ C2×C5×C121

36 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 16940

Conjugacy classes & character table

6050 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16940, 7);