Finite Group Databasebeta

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C2×C5×C7×D5×C11 #21440459

order7700
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C5×C7×C11 · Schur multiplier (H2) = C2

Aliases

direct productC2×C5×C7×D5×C11
unambiguous semidirect productC5⋊(C22×C5×C7×C11)
unambiguous semidirect product(C2×C5)⋊(C2×C5×C7×C11)

Splittings

Fitting, socleC2×C52×C7×C11 ⋊ C2
derivedC5 ⋊ C22×C5×C7×C11
HallC52×C7×C11 ⋊ C22
HallC52×C11 ⋊ C22×C7
HallC52×C7 ⋊ C22×C11
SylowC52 ⋊ C22×C7×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C7×C11D5
commutator, hypocenterC5C22×C5×C7×C11
FrattiniC1G
Fitting, socleC2×C52×C7×C11C2
LCSG ▷ C5
UCSC1 ◁ C2×C5×C7×C11

96 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3080 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C11×#3874, C2×C5×D5×C11×ΓL(1,𝔽8), C5×D3×C7×D5×C11, …
maximal normal subgroup ofC2×C5×D5×C11×ΓL(1,𝔽8), C2×C3×C5×C7×D5×C11
maximal quotient ofC5×D3×C7×D5×C11, C2×C3×C5×C7×D5×C11, C2×C5×C7×C11×D15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(7700, 123);