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C3×C7×Dic143 #26046418

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

Aliases

direct productC3×C7×Dic143
unambiguous semidirect productC11⋊(C3×C7×Dic13)

Splittings

derived, HallC11×C13 ⋊ C3×C4×C7
HallC3×C7×C11×C13 ⋊ C4
HallC7×C11×C13 ⋊ C3×C4
HallC3×C11×C13 ⋊ C4×C7
HallC3×C7×C13 ⋊ Dic11
HallC3×C7×C11 ⋊ Dic13
HallC7×C13 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×Dic13
HallC3×C13 ⋊ C7×Dic11
HallC3×C11 ⋊ C7×Dic13
SylowC13 ⋊ C3×C7×Dic11
SylowC11 ⋊ C3×C7×Dic13

Subgroups

subgroupG/H
center, hypercenterC2×C3×C7D143
commutator, hypocenterC11×C13C3×C4×C7
FrattiniC2C3×C7×D143
Fitting, socle, prime radicalC2×C3×C7×C11×C13C2
cosocleC2×C11×C13C2×C3×C7
LCSG ▷ C11×C13
UCSC1 ◁ C2×C3×C7

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3066 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC7×C9×Dic143, C7×C11⋊(Dic13⋊C9), C7⋊C9×Dic143, …
maximal normal subgroup ofC7×C9×Dic143, C7×C11⋊(Dic13⋊C9), C7⋊C9×Dic143, …
maximal quotient ofC7×C9×Dic143, C3×C7×Dic429, C32×C7×Dic143

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 8);