Finite Group Databasebeta

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C2×C5×C11×#3861 #30633570

order16170
isoclinismisoclinic class of #3861
automorphism?
homologyAbelianization (H1) = C2×C3×C5×C11 · Schur multiplier (H2) = C1

Aliases

direct productC2×C5×C11×#3861

Splittings

Fitting, socle, HallC2×C5×C72×C11 ⋊ C3
derived, SylowC72 ⋊ C2×C3×C5×C11
HallC5×C72×C11 ⋊ C2×C3
HallC2×C72×C11 ⋊ C3×C5
HallC72×C11 ⋊ C2×C3×C5
HallC2×C5×C72 ⋊ C3×C11
HallC5×C72 ⋊ C2×C3×C11
HallC2×C72 ⋊ C3×C5×C11

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11#3861
commutator, cosocle, hypocenterC72C2×C3×C5×C11
FrattiniC1G
Fitting, socleC2×C5×C72×C11C3
LCSG ▷ C72
UCSC1 ◁ C2×C5×C11

160 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5390

Conjugacy classes & character table

2090 conjugacy classes. The character table is too large to display.

Relationships

maximal subgroup ofC5×C11×#10596874, C5×C11⋊#10596874, C5×C11×#10596873, …
maximal normal subgroup ofC5×C11×#10596874, C5×C11⋊#10596874, C5×C11×#10596873, …
maximal quotient ofC4×C5×C11×#3861, C22×C5×C11×#3861

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(16170, 115);