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C23×#4007 #13044473

order1280
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC23×#4007
unambiguous semidirect productD5⋊(C22×#102)

Splittings

FittingC23×C5×D4 ⋊ C4
SylowC5 ⋊ C23×#102

Subgroups

subgroupG/H
centerC24C22⋊AGL(1,𝔽5)
commutatorC4×C5C24×C4
FrattiniC4C24×AGL(1,𝔽5)
FittingC23×C5×D4C4
socleC24×C5C22⋊C4
prime radicalC23×D4×D5C2
cosocleC4×D5C25
hypercenterC23×D4AGL(1,𝔽5)
hypocenterC5C23×#102
LCSG ▷ C4×C5 ▷ C2×C5 ▷ C5
UCSC1 ◁ C24 ◁ C23×C4 ◁ C23×D4

7646 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 320

Conjugacy classes & character table

152 conjugacy classes — view the full character table.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(1280, 1114741);