Finite Group Databasebeta

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C7×C11×C11⋊#157 #44479173

order30492
automorphism?
homologyAbelianization (H1) = C4×C7×C11 · Schur multiplier (H2) = C3

Aliases

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

Splittings

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

Subgroups

subgroupG/H
center, hypercenterC7×C11C11⋊#157
commutator, hypocenterC32×C11C4×C7×C11
FrattiniC1G
Fitting, socleC32×C7×C112C4
prime radicalC7×C112×C3⋊D3C2
cosocleC11×C3⋊D3C2×C7×C11
LCSG ▷ C32×C11
UCSC1 ◁ C7×C11

200 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 462

Conjugacy classes & character table

2772 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(30492, 396);