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C2×C5×#11715913 #21441071

order7770
automorphism?
homologyAbelianization (H1) = C2×C3×C5 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×#11715913

Splittings

Fitting, socle, HallC2×C5×C7×C37 ⋊ C3
derived, HallC7×C37 ⋊ C2×C3×C5
HallC5×C7×C37 ⋊ C2×C3
HallC2×C7×C37 ⋊ C3×C5
HallC2×C5×C37 ⋊ ΓL(1,𝔽8)
HallC5×C37 ⋊ C2×ΓL(1,𝔽8)
HallC2×C37 ⋊ C5×ΓL(1,𝔽8)
HallC2×C5×C7 ⋊ C37⋊C3
SylowC37 ⋊ C2×C5×ΓL(1,𝔽8)
HallC5×C7 ⋊ C2×C37⋊C3
HallC2×C7 ⋊ C5×C37⋊C3
SylowC7 ⋊ C2×C5×C37⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C5#11715913
commutator, hypocenterC7×C37C2×C3×C5
FrattiniC1G
Fitting, socleC2×C5×C7×C37C3
LCSG ▷ C7×C37
UCSC1 ◁ C2×C5

32 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

890 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofC4×C5×#11715913, C5×#15690920, C5×#15690924, …
maximal normal subgroup ofC4×C5×#11715913, C5×#15690920, C5×#15690924, …
maximal quotient ofC4×C5×#11715913, C22×C5×#11715913, C2×C5×#14556419, …

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7770, 4);