Finite Group Databasebeta

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C11×C7⋊#66772 #39910458

order26180
automorphism?
homologyAbelianization (H1) = C4×C11 · Schur multiplier (H2) = C1

Aliases

direct productC11×C7⋊#66772
unambiguous semidirect productC7⋊(C11×#66772)

Splittings

Fitting, socle, HallC5×C7×C11×C17 ⋊ C4
derived, HallC5×C7×C17 ⋊ C4×C11
HallC7×C11×C17 ⋊ Dic5
HallC5×C11×C17 ⋊ Dic7
HallC5×C7×C11 ⋊ #595
HallC11×C17 ⋊ Dic35
HallC7×C17 ⋊ C11×Dic5
HallC5×C17 ⋊ C11×Dic7
HallC7×C11 ⋊ #66772
HallC5×C11 ⋊ C7⋊#595
HallC5×C7 ⋊ C11×#595
SylowC17 ⋊ C11×Dic35
SylowC7 ⋊ C11×#66772
SylowC5 ⋊ C11×C7⋊#595

Subgroups

subgroupG/H
center, hypercenterC11C7⋊#66772
commutator, hypocenterC5×C7×C17C4×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C17C4
prime radicalC5×C7×C11×D17C2
cosocleC5×C7×D17C2×C11
LCSG ▷ C5×C7×C17
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6545

Conjugacy classes & character table

1958 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 80);