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C2×C72×D5×C11 #24924796

order10780
isoclinismisoclinic class of D5
automorphism?
homologyAbelianization (H1) = C22×C72×C11 · Schur multiplier (H2) = C2×C7

Aliases

direct productC2×C72×D5×C11
unambiguous semidirect productC5⋊(C22×C72×C11)
unambiguous semidirect product(C2×C5)⋊(C2×C72×C11)

Splittings

Fitting, socleC2×C5×C72×C11 ⋊ C2
derived, SylowC5 ⋊ C22×C72×C11
HallC5×C72×C11 ⋊ C22
HallC5×C72 ⋊ C22×C11
HallC5×C11 ⋊ C22×C72

Subgroups

subgroupG/H
center, hypercenterC2×C72×C11D5
commutator, cosocle, hypocenterC5C22×C72×C11
FrattiniC1G
Fitting, socleC2×C5×C72×C11C2
LCSG ▷ C5
UCSC1 ◁ C2×C72×C11

200 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

4312 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×D5×C11×ΓL(1,𝔽8), C2×D5×C11×#3861, C2×D5×C11×#3862, …
maximal normal subgroup ofC2×C7×D5×C11×ΓL(1,𝔽8), C2×D5×C11×#3861, C2×D5×C11×#3862, …
maximal quotient ofD3×C72×D5×C11, C2×C3×C72×D5×C11, C2×C72×C11×D15

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 109);