Finite Group Databasebeta

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C5×C7⋊(C11⋊#595) #39910428

order26180
automorphism?
homologyAbelianization (H1) = C4×C5 · Schur multiplier (H2) = C1

Aliases

direct productC5×C7⋊(C11⋊#595)
unambiguous semidirect productC7⋊(C5×C11⋊#595)

Splittings

Fitting, socle, HallC5×C7×C11×C17 ⋊ C4
derived, HallC7×C11×C17 ⋊ C4×C5
HallC5×C11×C17 ⋊ Dic7
HallC5×C7×C17 ⋊ Dic11
HallC5×C7×C11 ⋊ #595
HallC11×C17 ⋊ C5×Dic7
HallC7×C17 ⋊ C5×Dic11
HallC5×C17 ⋊ Dic77
HallC7×C11 ⋊ C5×#595
HallC5×C11 ⋊ C7⋊#595
HallC5×C7 ⋊ C11⋊#595
SylowC17 ⋊ C5×Dic77
SylowC11 ⋊ C5×C7⋊#595
SylowC7 ⋊ C5×C11⋊#595

Subgroups

subgroupG/H
center, hypercenterC5C7⋊(C11⋊#595)
commutator, hypocenterC7×C11×C17C4×C5
FrattiniC1G
Fitting, socleC5×C7×C11×C17C4
prime radicalC5×C7×C11×D17C2
cosocleC7×C11×D17C2×C5
LCSG ▷ C7×C11×C17
UCSC1 ◁ C5

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6545

Conjugacy classes & character table

1940 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 50);