Finite Group Databasebeta

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C2×C11×C13×C11⋊C5 #30628524

order15730
isoclinismisoclinic class of C11⋊C5
automorphism?
homologyAbelianization (H1) = C2×C5×C11×C13 · Schur multiplier (H2) = C1

Aliases

direct productC2×C11×C13×C11⋊C5
unambiguous semidirect product(C2×C11)⋊(C5×C11×C13)
unambiguous semidirect product(C2×C11×C13)⋊(C5×C11)

Splittings

Fitting, socle, HallC2×C112×C13 ⋊ C5
derivedC11 ⋊ C2×C5×C11×C13
HallC112×C13 ⋊ C2×C5
HallC2×C112 ⋊ C5×C13
SylowC112 ⋊ C2×C5×C13

Subgroups

subgroupG/H
center, hypercenterC2×C11×C13C11⋊C5
commutator, cosocle, hypocenterC11C2×C5×C11×C13
FrattiniC1G
Fitting, socleC2×C112×C13C5
LCSG ▷ C11
UCSC1 ◁ C2×C11×C13

40 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1430

Conjugacy classes & character table

2002 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC11×C13×Dic11⋊C5, C11×(C11⋊C5)⋊Dic13, C11×Dic13×C11⋊C5, …
maximal normal subgroup ofC11×C13×Dic11⋊C5, C11×(C11⋊C5)⋊Dic13, C11×Dic13×C11⋊C5, …
maximal quotient ofC4×C11×C13×C11⋊C5, C22×C11×C13×C11⋊C5

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15730, 41);