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C2×C5×C7⋊D77 #24924797

order10780
automorphism?
homologyAbelianization (H1) = C22×C5 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C5×C7⋊D77
unambiguous semidirect product(C2×C7)⋊(C5×D77)

Splittings

Fitting, socleC2×C5×C72×C11 ⋊ C2
derived, HallC72×C11 ⋊ C22×C5
HallC5×C72×C11 ⋊ C22
HallC5×C72 ⋊ C2×D11
HallC5×C11 ⋊ C2×C7⋊D7
SylowC72 ⋊ C2×C5×D11
SylowC11 ⋊ C2×C5×C7⋊D7

Subgroups

subgroupG/H
center, hypercenterC2×C5C7⋊D77
commutator, cosocle, hypocenterC72×C11C22×C5
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2
LCSG ▷ C72×C11
UCSC1 ◁ C2×C5

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

2710 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C5×C11⋊(ΓL(1,𝔽8)⋊D7), C2×C5×C11⋊#64424, C2×C5×C11⋊#64425, …
maximal normal subgroup ofC2×C5×C11⋊(ΓL(1,𝔽8)⋊D7), C2×C5×C11⋊#64424, C2×C5×C11⋊#64425, …
maximal quotient ofC5×D3×C7⋊D77, C2×C3×C5×C7⋊D77, C2×C5×C3⋊(C7⋊D77)

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 110);