Finite Group Databasebeta

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C2×2−1+4×#6923 #30626730

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

Aliases

direct productC2×2−1+4×#6923
unambiguous semidirect productD61⋊(C4×2−1+4)

Splittings

FittingC2×2−1+4×C61 ⋊ C4
SylowC61 ⋊ C2×C4×2−1+4

Subgroups

subgroupG/H
centerC22C24×#6923
commutatorC2×C61C25×C4
FrattiniC2C25×#6923
FittingC2×2−1+4×C61C4
socleC22×C61C24×C4
prime radicalC2×2−1+4×D61C2
cosocleC2×D61C26
hypercenterC2×2−1+4#6923
hypocenterC61C2×C4×2−1+4
LCSG ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×2−1+4

11210 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1952

Conjugacy classes & character table

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

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(15616, 1116285);