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C2×#21461665 #30614910

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C28

Aliases

direct productC2×#21461665
unambiguous semidirect productD61⋊#1792

Splittings

FittingC2×H(5,𝔽2)×C61 ⋊ C4
SylowC61 ⋊ C2×#1792

Subgroups

subgroupG/H
centerC22#16840703
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC2×H(5,𝔽2)×C61C4
socleC22×C61#379
prime radicalC2×H(5,𝔽2)×D61C2
cosocleC2×C4×D61C24
hypercenterC2×H(5,𝔽2)#6923
hypocenterC61C2×#1792
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×H(5,𝔽2)

4114 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 976

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1104465);