Finite Group Databasebeta

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C11×C7⋊(C11⋊#157) #44479177

order30492
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C3

Aliases

direct productC11×C7⋊(C11⋊#157)
unambiguous semidirect productC7⋊(C11×C11⋊#157)
unambiguous semidirect productC11⋊(C11×C7⋊#157)

Splittings

Fitting, socle, HallC32×C7×C112 ⋊ C4
derivedC32×C7×C11 ⋊ C4×C11
HallC32×C112 ⋊ Dic7
HallC7×C112 ⋊ #157
SylowC112 ⋊ C7⋊#157
HallC32×C7 ⋊ C11×Dic11
SylowC32 ⋊ C11×Dic77
SylowC7 ⋊ C11×C11⋊#157

Subgroups

subgroupG/H
center, hypercenterC11C7⋊(C11⋊#157)
commutator, hypocenterC32×C7×C11C4×C11
FrattiniC1G
Fitting, socleC32×C7×C112C4
prime radicalC7×C112×C3⋊D3C2
cosocleC7×C11×C3⋊D3C2×C11
LCSG ▷ C32×C7×C11
UCSC1 ◁ C11

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

2574 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 400);