Finite Group Databasebeta

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C7×C11×Dic39 #26046424

order12012
isoclinismisoclinic class of D39
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C1

Aliases

direct productC7×C11×Dic39
unambiguous semidirect productC3⋊(C7×C11×Dic13)

Splittings

derived, HallC3×C13 ⋊ C4×C7×C11
HallC3×C7×C11×C13 ⋊ C4
HallC7×C11×C13 ⋊ Dic3
HallC3×C11×C13 ⋊ C4×C7
HallC3×C7×C13 ⋊ C4×C11
HallC3×C7×C11 ⋊ Dic13
HallC11×C13 ⋊ C7×Dic3
HallC7×C13 ⋊ C11×Dic3
HallC3×C11 ⋊ C7×Dic13
HallC3×C7 ⋊ C11×Dic13
SylowC13 ⋊ C7×C11×Dic3
SylowC3 ⋊ C7×C11×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C7×C11D39
commutator, hypocenterC3×C13C4×C7×C11
FrattiniC2C7×C11×D39
Fitting, socle, prime radicalC2×C3×C7×C11×C13C2
cosocleC2×C3×C13C2×C7×C11
LCSG ▷ C3×C13
UCSC1 ◁ C2×C7×C11

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3234 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C11×Dic117, C7×C11×C3⋊(Dic13⋊C3), C11×C3⋊#11763957, …
maximal normal subgroup ofC7×C11×C3⋊(Dic13⋊C3), C11×C3⋊#11763957, C11×C3⋊#11763958, …
maximal quotient ofC7×C11×Dic117, C7×C11×C3⋊Dic39, C3×C7×C11×Dic39

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 14);