Finite Group Databasebeta

← Prev (#24924729) Next (#24924731) →

C4×C72×C11⋊C5 #24924730

order10780
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C4×C5×C72 · Schur multiplier (H2) = C7

Aliases

direct productC4×C72×C11⋊C5
unambiguous semidirect product(C4×C11)⋊(C5×C72)
unambiguous semidirect product(C4×C7×C11)⋊(C5×C7)
unambiguous semidirect product(C4×C72×C11)⋊C5

Splittings

Fitting, HallC4×C72×C11 ⋊ C5
derived, SylowC11 ⋊ C4×C5×C72
HallC72×C11 ⋊ C4×C5
HallC4×C11 ⋊ C5×C72

Subgroups

subgroupG/H
center, hypercenterC4×C72C11⋊C5
commutator, hypocenterC11C4×C5×C72
FrattiniC2C2×C72×C11⋊C5
FittingC4×C72×C11C5
socleC2×C72×C11C2×C5
prime radicalC2×C72×C11⋊C5C2
cosocleC2×C11C2×C5×C72
LCSG ▷ C11
UCSC1 ◁ C4×C72

120 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1372 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C7×ΓL(1,𝔽8)×C11⋊C5, C4×C11⋊C5×#3861, C4×C11⋊C5×#3862, …
maximal normal subgroup ofC4×C7×ΓL(1,𝔽8)×C11⋊C5, C4×C11⋊C5×#3861, C4×C11⋊C5×#3862, …
maximal quotient ofC72×Dic3×C11⋊C5, C3×C4×C72×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(10780, 43);