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C4×#16839933 #29685905

order15616
automorphism?
homologyAbelianization (H1) = C23×C4 · Schur multiplier (H2) = C26

Aliases

direct productC4×#16839933

Splittings

FittingC4×AGL(1,ℤ/8)×C61 ⋊ C2
SylowC61 ⋊ C4×#454

Subgroups

subgroupG/H
centerC2×C4#14519745
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC4×AGL(1,ℤ/8)×C61C2
socleC22×C61C2×#120
prime radicalC2×#16839933C2
cosocleC22×C4×C61C24
hypercenterC4×AGL(1,ℤ/8)D61
hypocenterC61C4×#454
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C4×AGL(1,ℤ/8)

1390 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 3904

Conjugacy classes & character table

1384 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 175460);