Finite Group Databasebeta

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C11×#15692571 #49114371

order36036
automorphism?
homologyAbelianization (H1) = C4×C9×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×#15692571

Splittings

derived, HallC7×C13 ⋊ C4×C9×C11
HallC11×#11717941 ⋊ C4
HallC11×Dic91 ⋊ C9
HallC7×C11×C13 ⋊ C4×C9
Hall#11717941 ⋊ C4×C11
HallDic91 ⋊ C9×C11
HallC11×C13 ⋊ Dic7⋊C9
HallC7×C11 ⋊ Dic13⋊C9
SylowC13 ⋊ C11×Dic7⋊C9
SylowC7 ⋊ C11×Dic13⋊C9

Subgroups

subgroupG/H
center, hypercenterC2×C3×C11#10587722
commutator, hypocenterC7×C13C4×C9×C11
FrattiniC2×C3C11×#10587722
Fitting, socle, prime radicalC2×C3×C7×C11×C13C2×C3
cosocleC2×C3×C7×C13C2×C3×C11
LCSG ▷ C7×C13
UCSC1 ◁ C2×C3×C11

72 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 36036

Conjugacy classes & character table

1386 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(36036, 39);