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C3×Dic1001 #26046422

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

Aliases

direct productC3×Dic1001
unambiguous semidirect productC11⋊(C3×Dic91)

Splittings

derived, HallC7×C11×C13 ⋊ C3×C4
HallC3×C7×C11×C13 ⋊ C4
HallC3×C11×C13 ⋊ Dic7
HallC3×C7×C13 ⋊ Dic11
HallC3×C7×C11 ⋊ Dic13
HallC11×C13 ⋊ C3×Dic7
HallC7×C13 ⋊ C3×Dic11
HallC7×C11 ⋊ C3×Dic13
HallC3×C13 ⋊ Dic77
HallC3×C11 ⋊ Dic91
HallC3×C7 ⋊ Dic143
SylowC13 ⋊ C3×Dic77
SylowC11 ⋊ C3×Dic91
SylowC7 ⋊ C3×Dic143

Subgroups

subgroupG/H
center, hypercenterC2×C3D1001
commutator, hypocenterC7×C11×C13C3×C4
FrattiniC2C3×D1001
Fitting, socle, prime radicalC2×C3×C7×C11×C13C2
cosocleC2×C7×C11×C13C2×C3
LCSG ▷ C7×C11×C13
UCSC1 ◁ C2×C3

48 conjugacy classes of subgroups.

Full subgroup data →

Conjugacy classes & character table

3012 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC9×Dic1001, C11⋊#15692563, C11⋊((C7⋊C9)⋊Dic13), …
maximal normal subgroup ofC9×Dic1001, C11⋊#15692563, C11⋊((C7⋊C9)⋊Dic13), …
maximal quotient ofC9×Dic1001, C3×Dic3003, C32×Dic1001

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(12012, 12);