Finite Group Databasebeta

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C4×#16840565 #30544230

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C29

Aliases

direct productC4×#16840565

Splittings

FittingC4×H(5,𝔽2)×C61 ⋊ C2
SylowC61 ⋊ C4×#576

Subgroups

subgroupG/H
centerC2×C4C22×C22⋊D61
commutatorC4×C61C24×C4
FrattiniC2×C4C24×D61
FittingC4×H(5,𝔽2)×C61C2
socleC22×C61C23×D4
prime radicalC2×#16840565C2
cosocleC2×C4×C61C25
hypercenterC4×H(5,𝔽2)D61
hypocenterC61C4×#576
LCSG ▷ C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ C4×H(5,𝔽2)

2826 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2128 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1033785);