Finite Group Databasebeta

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C2×C7×C23×C11⋊C5 #31799309

order17710
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C5×C7×C23 · Schur multiplier (H2) = C1

Aliases

direct productC2×C7×C23×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C5×C7×C23)
unambiguous semidirect product(C2×C7×C11)⋊(C5×C23)
unambiguous semidirect product(C2×C11×C23)⋊(C5×C7)
unambiguous semidirect product(C2×C7×C11×C23)⋊C5

Splittings

Fitting, socle, HallC2×C7×C11×C23 ⋊ C5
derived, SylowC11 ⋊ C2×C5×C7×C23
HallC7×C11×C23 ⋊ C2×C5
HallC2×C11×C23 ⋊ C5×C7
HallC11×C23 ⋊ C2×C5×C7
HallC2×C7×C11 ⋊ C5×C23
HallC7×C11 ⋊ C2×C5×C23
HallC2×C11 ⋊ C5×C7×C23

Subgroups

subgroupG/H
center, hypercenterC2×C7×C23C11⋊C5
commutator, cosocle, hypocenterC11C2×C5×C7×C23
FrattiniC1G
Fitting, socleC2×C7×C11×C23C5
LCSG ▷ C11
UCSC1 ◁ C2×C7×C23

32 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3542

Conjugacy classes & character table

2254 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC4×C7×C23×C11⋊C5, C7×C11⋊C5×Dic23, C7×C23×Dic11⋊C5, …
maximal normal subgroup ofC4×C7×C23×C11⋊C5, C7×C11⋊C5×Dic23, C7×C23×Dic11⋊C5, …
maximal quotient ofC4×C7×C23×C11⋊C5, C22×C7×C23×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(17710, 3);