Finite Group Databasebeta

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C5×C11×C17×Dic7 #39910384

order26180
automorphism?
homologyAbelianization (H1) = C4×C5×C11×C17 · Schur multiplier (H2) = C1

Aliases

direct productC5×C11×C17×Dic7
unambiguous semidirect productC7⋊(C4×C5×C11×C17)

Splittings

derived, SylowC7 ⋊ C4×C5×C11×C17
HallC5×C7×C11×C17 ⋊ C4
HallC7×C11×C17 ⋊ C4×C5
HallC5×C7×C17 ⋊ C4×C11
HallC5×C7×C11 ⋊ C4×C17
HallC7×C17 ⋊ C4×C5×C11
HallC7×C11 ⋊ C4×C5×C17
HallC5×C7 ⋊ C4×C11×C17

Subgroups

subgroupG/H
center, hypercenterC2×C5×C11×C17D7
commutator, hypocenterC7C4×C5×C11×C17
FrattiniC2C5×C11×D7×C17
Fitting, socle, prime radicalC2×C5×C7×C11×C17C2
cosocleC2×C7C2×C5×C11×C17
LCSG ▷ C7
UCSC1 ◁ C2×C5×C11×C17

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 26180

Conjugacy classes & character table

9350 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(26180, 6);