Finite Group Databasebeta

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C22×#16840713 #30624574

order15616
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C210

Aliases

direct productC22×#16840713
unambiguous semidirect productD61⋊(C2×#389)

Splittings

FittingC22×C4⋊C4×C61 ⋊ C4
SylowC61 ⋊ C22×#389

Subgroups

subgroupG/H
centerC24C22×#6923
commutatorC22×C61C24×C4
FrattiniC22C24×#6923
FittingC22×C4⋊C4×C61C4
socleC24×C61C22×C4
prime radicalC24×D61C23
cosocleC22×D61C25
hypercenterC22×C4⋊C4#6923
hypocenterC61C22×#389
LCSG ▷ C22×C61 ▷ C61
UCSC1 ◁ C24 ◁ C22×C4⋊C4

4894 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, 1114129);