Finite Group Databasebeta

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C11×#15668135 #44535501

order31350
automorphism?
homologyAbelianization (H1) = C2×C3×C11 · Schur multiplier (H2) = C5

Aliases

direct productC11×#15668135

Splittings

Fitting, socle, HallC52×C11×C19 ⋊ C2×C3
derived, HallC52×C19 ⋊ C2×C3×C11
HallC11×C19×C52⋊C3 ⋊ C2
HallC11×C5⋊D95 ⋊ C3
HallC19×C52⋊C3 ⋊ C2×C11
HallC5⋊D95 ⋊ C3×C11
HallC11×C52⋊C3 ⋊ D19
HallC52×C11 ⋊ C3×D19
HallC11×C19 ⋊ (C5⋊D5)⋊C3
HallC52⋊C3 ⋊ C11×D19
SylowC52 ⋊ C3×C11×D19
SylowC19 ⋊ C11×(C5⋊D5)⋊C3

Subgroups

subgroupG/H
center, hypercenterC11#15668135
commutator, cosocle, hypocenterC52×C19C2×C3×C11
FrattiniC1G
Fitting, socleC52×C11×C19C2×C3
LCSG ▷ C52×C19
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3135

Conjugacy classes & character table

1199 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(31350, 74);