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C2×D5⋊(C7⋊C8) #11765355

order1120
isoclinismisoclinic class of C7⋊AGL(1,𝔽5)
automorphism?
homologyAbelianization (H1) = C22×C8 · Schur multiplier (H2) = C23

Aliases

direct productC2×D5⋊(C7⋊C8)
unambiguous semidirect productD5⋊(C2×C7⋊C8)

Splittings

derived, HallC5×C7 ⋊ C22×C8
SylowC7 ⋊ C2×D5⋊C8
SylowC5 ⋊ C22×C7⋊C8

Subgroups

subgroupG/H
center, hypercenterC2×C4C7⋊AGL(1,𝔽5)
commutator, hypocenterC5×C7C22×C8
FrattiniC2C22×C7⋊AGL(1,𝔽5)
FittingC2×C4×C5×C7C4
socleC22×C5×C7C2×C4
prime radicalC22×C7×D5C4
cosocleC7×Dic5C23
LCSG ▷ C5×C7
UCSC1 ◁ C2×C4

152 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 560

Conjugacy classes & character table

136 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1120, 961);