Finite Group Databasebeta

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C7×Dic429 #26046426

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

Aliases

direct productC7×Dic429
unambiguous semidirect productC3⋊(C7×Dic143)
unambiguous semidirect productC11⋊(C7×Dic39)

Splittings

derived, HallC3×C11×C13 ⋊ C4×C7
HallC3×C7×C11×C13 ⋊ C4
HallC7×C11×C13 ⋊ Dic3
HallC3×C7×C13 ⋊ Dic11
HallC3×C7×C11 ⋊ Dic13
HallC11×C13 ⋊ C7×Dic3
HallC7×C13 ⋊ Dic33
HallC7×C11 ⋊ Dic39
HallC3×C13 ⋊ C7×Dic11
HallC3×C11 ⋊ C7×Dic13
HallC3×C7 ⋊ Dic143
SylowC13 ⋊ C7×Dic33
SylowC11 ⋊ C7×Dic39
SylowC3 ⋊ C7×Dic143

Subgroups

subgroupG/H
center, hypercenterC2×C7D429
commutator, hypocenterC3×C11×C13C4×C7
FrattiniC2C7×D429
Fitting, socle, prime radicalC2×C3×C7×C11×C13C2
cosocleC2×C3×C11×C13C2×C7
LCSG ▷ C3×C11×C13
UCSC1 ◁ C2×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3024 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×Dic1287, C7×C3⋊(C11⋊(Dic13⋊C3)), C3⋊(C11⋊#11763957), …
maximal normal subgroup ofC7×C3⋊(C11⋊(Dic13⋊C3)), C3⋊(C11⋊#11763957), C3⋊(C11⋊#11763958), …
maximal quotient ofC7×Dic1287, C7×C3⋊Dic429, C3×C7×Dic429

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 16);