Finite Group Databasebeta

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C4×#16840597 #30586624

order15616
automorphism?
homologyAbelianization (H1) = C25×C4 · Schur multiplier (H2) = C214

Aliases

direct productC4×#16840597

Splittings

FittingC4×H(5,𝔽2)×C61 ⋊ C2
SylowC61 ⋊ C4×#585

Subgroups

subgroupG/H
centerC2×C4C24×D61
commutatorC2×C61C25×C4
FrattiniC22C25×D61
FittingC4×H(5,𝔽2)×C61C2
socle, cosocleC22×C61C26
prime radicalC2×#16840597C2
hypercenterC4×H(5,𝔽2)D61
hypocenterC61C4×#585
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×H(5,𝔽2)

11346 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

2176 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1076179);