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C2×C5×C7×C37⋊C3 #21441069

order7770
isoclinismisoclinic class of C37⋊C3
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C7 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C7×C37⋊C3
unambiguous semidirect product(C2×C37)⋊(C3×C5×C7)
unambiguous semidirect product(C2×C5×C37)⋊(C3×C7)

Splittings

Fitting, socle, HallC2×C5×C7×C37 ⋊ C3
derived, SylowC37 ⋊ C2×C3×C5×C7
HallC5×C7×C37 ⋊ C2×C3
HallC2×C7×C37 ⋊ C3×C5
HallC2×C5×C37 ⋊ C3×C7
HallC7×C37 ⋊ C2×C3×C5
HallC5×C37 ⋊ C2×C3×C7
HallC2×C37 ⋊ C3×C5×C7

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7C37⋊C3
commutator, hypocenterC37C2×C3×C5×C7
FrattiniC1G
Fitting, socleC2×C5×C7×C37C3
LCSG ▷ C37
UCSC1 ◁ C2×C5×C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1050 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C5×C7×C37⋊C3, C5×C7×Dic37⋊C3, C5×Dic7×C37⋊C3, …
maximal normal subgroup ofC4×C5×C7×C37⋊C3, C5×C7×Dic37⋊C3, C5×Dic7×C37⋊C3, …
maximal quotient ofC4×C5×C7×C37⋊C3, C22×C5×C7×C37⋊C3, C2×C5×C7×#66524, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7770, 2);