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C7×D5×C37⋊C3 #21441100

order7770
automorphism?
homologyAbelianization (H1) = C2×C3×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×D5×C37⋊C3
unambiguous semidirect productC5⋊(C2×C7×C37⋊C3)
unambiguous semidirect product(D5×C37)⋊(C3×C7)

Splittings

Fitting, socle, HallC5×C7×C37 ⋊ C2×C3
derived, HallC5×C37 ⋊ C2×C3×C7
HallC5×C7×C37⋊C3 ⋊ C2
HallC7×D5×C37 ⋊ C3
HallC5×C37⋊C3 ⋊ C2×C7
HallD5×C37 ⋊ C3×C7
HallC7×C37 ⋊ C3×D5
SylowC37 ⋊ C3×C7×D5
HallC5×C7 ⋊ C2×C37⋊C3
SylowC5 ⋊ C2×C7×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC7D5×C37⋊C3
commutator, hypocenterC5×C37C2×C3×C7
FrattiniC1G
Fitting, socleC5×C7×C37C2×C3
LCSG ▷ C5×C37
UCSC1 ◁ C7

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

420 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC7×#10625193⋊C3, C7×AGL(1,𝔽5)×C37⋊C3, #29509590, …
maximal normal subgroup ofC7×#10625193⋊C3, C7×AGL(1,𝔽5)×C37⋊C3, #29509590, …
maximal quotient ofC7×Dic5×C37⋊C3, C2×C7×D5×C37⋊C3, C7×D5×#66524, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7770, 33);