Finite Group Databasebeta

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C11×C7⋊#66774 #39910445

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

Aliases

direct productC11×C7⋊#66774
unambiguous semidirect productC7⋊(C11×#66774)

Splittings

Fitting, socle, HallC5×C7×C11×C17 ⋊ C4
derived, HallC5×C7×C17 ⋊ C4×C11
HallC7×C11×C17 ⋊ AGL(1,𝔽5)
HallC5×C11×C17 ⋊ Dic7
HallC5×C7×C11 ⋊ Dic17
HallC11×C17 ⋊ C7⋊AGL(1,𝔽5)
HallC7×C17 ⋊ C11×AGL(1,𝔽5)
HallC5×C17 ⋊ C11×Dic7
HallC7×C11 ⋊ #66774
HallC5×C11 ⋊ Dic119
HallC5×C7 ⋊ C11×Dic17
SylowC17 ⋊ C11×C7⋊AGL(1,𝔽5)
SylowC7 ⋊ C11×#66774
SylowC5 ⋊ C11×Dic119

Subgroups

subgroupG/H
center, hypercenterC11C7⋊#66774
commutator, hypocenterC5×C7×C17C4×C11
FrattiniC1G
Fitting, socleC5×C7×C11×C17C4
prime radicalC7×D5×C11×C17C2
cosocleC7×D5×C17C2×C11
LCSG ▷ C5×C7×C17
UCSC1 ◁ C11

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 6545

Conjugacy classes & character table

2651 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 67);