Finite Group Databasebeta

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C4×#16840711 #30608636

order15616
automorphism?
homologyAbelianization (H1) = C22×C42 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#16840711

Splittings

FittingC4×C4⋊C4×C61 ⋊ C4
SylowC61 ⋊ C4×#387

Subgroups

subgroupG/H
centerC22×C4C22×#6923
commutatorC22×C61C22×C42
FrattiniC23C23×#6923
FittingC4×C4⋊C4×C61C4
socleC23×C61C23×C4
prime radical, cosocleC23×D61C24
hypercenterC4×C4⋊C4#6923
hypocenterC61C4×#387
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C4×C4⋊C4

1742 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1098191);