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C7×C13⋊C3×Dic11 #26046435

order12012
automorphism?
homologyAbelianization (H1) = C3×C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×C13⋊C3×Dic11
unambiguous semidirect productC11⋊(C4×C7×C13⋊C3)
unambiguous semidirect product(C13×Dic11)⋊(C3×C7)

Splittings

derived, HallC11×C13 ⋊ C3×C4×C7
HallC7×C13×Dic11 ⋊ C3
HallC7×C11×C13⋊C3 ⋊ C4
HallC7×C11×C13 ⋊ C3×C4
HallC13×Dic11 ⋊ C3×C7
HallC11×C13⋊C3 ⋊ C4×C7
HallC7×C13 ⋊ C3×Dic11
HallC7×C11 ⋊ C4×C13⋊C3
SylowC13 ⋊ C3×C7×Dic11
SylowC11 ⋊ C4×C7×C13⋊C3

Subgroups

subgroupG/H
center, hypercenterC2×C7D11×C13⋊C3
commutator, hypocenterC11×C13C3×C4×C7
FrattiniC2C7×D11×C13⋊C3
Fitting, socleC2×C7×C11×C13C2×C3
prime radicalC2×C7×C11×C13⋊C3C2
cosocleC2×C11×C13C2×C3×C7
LCSG ▷ C11×C13
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

686 conjugacy classes — view the full character table.

Relationships

maximal subgroup ofΓL(1,𝔽8)×C13⋊C3×Dic11, C3×C7×C13⋊C3×Dic11, C7×C13⋊C3×Dic33
maximal normal subgroup ofΓL(1,𝔽8)×C13⋊C3×Dic11, C3×C7×C13⋊C3×Dic11
maximal quotient ofC7×Dic11×C13⋊C9, C3×C7×C13⋊C3×Dic11, C7×C13⋊C3×Dic33

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 25);