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C7×Dic1287 #49114348

order36036
automorphism?
homologyAbelianization (H1) = C4×C7 · Schur multiplier (H2) = C1

Aliases

direct productC7×Dic1287
unambiguous semidirect productC9⋊(C7×Dic143)
unambiguous semidirect productC11⋊(C7×Dic117)

Splittings

derived, HallC9×C11×C13 ⋊ C4×C7
HallC7×C9×C11×C13 ⋊ C4
HallC7×C11×C13 ⋊ Dic9
HallC7×C9×C13 ⋊ Dic11
HallC7×C9×C11 ⋊ Dic13
HallC11×C13 ⋊ C7×Dic9
HallC9×C13 ⋊ C7×Dic11
HallC9×C11 ⋊ C7×Dic13
HallC7×C13 ⋊ Dic99
HallC7×C11 ⋊ Dic117
HallC7×C9 ⋊ Dic143
SylowC13 ⋊ C7×Dic99
SylowC11 ⋊ C7×Dic117
SylowC9 ⋊ C7×Dic143

Subgroups

subgroupG/H
center, hypercenterC2×C7D1287
commutator, hypocenterC9×C11×C13C4×C7
FrattiniC2×C3C7×D429
FittingC2×C7×C9×C11×C13C2
socle, prime radicalC2×C3×C7×C11×C13D3
cosocleC2×C9×C11×C13C2×C7
LCSG ▷ C9×C11×C13
UCSC1 ◁ C2×C7

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36036

Conjugacy classes & character table

9030 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 16);