Finite Group Databasebeta

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C4×#16840639 #30602326

order15616
automorphism?
homologyAbelianization (H1) = C43 · Schur multiplier (H2) = C23×C42

Aliases

direct productC4×#16840639

Splittings

FittingC4×C22⋊C4×C61 ⋊ C4
SylowC61 ⋊ C4×#342

Subgroups

subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC22×C61C43
FrattiniC24C22×#6923
FittingC4×C22⋊C4×C61C4
socleC22×C61C2×#95
prime radical, cosocleC24×D61C23
hypercenterC4×C22⋊C4#6923
hypocenterC61C4×#342
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C4×C22⋊C4

1482 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1091881);