Finite Group Databasebeta

← Prev (#44479271) Next (#44479273) →

C2×C11×C3⋊D231 #44479272

order30492
automorphism?
homologyAbelianization (H1) = C22×C11 · Schur multiplier (H2) = C2×C3

Aliases

direct productC2×C11×C3⋊D231
unambiguous semidirect product(C2×C3)⋊(C11×D231)
unambiguous semidirect product(C2×C7)⋊(C11×C3⋊D33)
unambiguous semidirect product(C2×C11)⋊(C11×C3⋊D21)

Splittings

Fitting, socleC2×C32×C7×C112 ⋊ C2
derivedC32×C7×C11 ⋊ C22×C11
HallC32×C7×C112 ⋊ C22
HallC32×C112 ⋊ C2×D7
HallC7×C112 ⋊ C2×C3⋊D3
SylowC112 ⋊ C2×C3⋊D21
HallC32×C7 ⋊ C2×C11×D11
SylowC32 ⋊ C2×C11×D77
SylowC7 ⋊ C2×C11×C3⋊D33

Subgroups

subgroupG/H
center, hypercenterC2×C11C3⋊D231
commutator, cosocle, hypocenterC32×C7×C11C22×C11
FrattiniC1G
Fitting, socleC2×C32×C7×C112C2
LCSG ▷ C32×C7×C11
UCSC1 ◁ C2×C11

360 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2772

Conjugacy classes & character table

7656 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 495);