Finite Group Databasebeta

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C7×C23×C11⋊C5 #22579684

order8855
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C5×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC7×C23×C11⋊C5
unambiguous semidirect productC11⋊(C5×C7×C23)
unambiguous semidirect product(C7×C11)⋊(C5×C23)
unambiguous semidirect product(C11×C23)⋊(C5×C7)
unambiguous semidirect product(C7×C11×C23)⋊C5

Splittings

Fitting, socle, HallC7×C11×C23 ⋊ C5
derived, SylowC11 ⋊ C5×C7×C23
HallC11×C23 ⋊ C5×C7
HallC7×C11 ⋊ C5×C23

Subgroups

subgroupG/H
center, hypercenterC7×C23C11⋊C5
commutator, hypocenterC11C5×C7×C23
FrattiniC1G
Fitting, socleC7×C11×C23C5
LCSG ▷ C11
UCSC1 ◁ C7×C23

16 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

1127 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC2×C7×C23×C11⋊C5, C7×D23×C11⋊C5, C7×C23×AGL(1,𝔽11), …
maximal normal subgroup ofC2×C7×C23×C11⋊C5, C7×D23×C11⋊C5, C7×C23×AGL(1,𝔽11), …
maximal quotient ofC2×C7×C23×C11⋊C5, C3×C7×C23×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(8855, 3);